path: root/doc/rfc/rfc9500.txt

Internet Engineering Task Force (IETF)                        P. Gutmann
Request for Comments: 9500                        University of Auckland
Category: Informational                                       C. Bonnell
ISSN: 2070-1721                                                 DigiCert
                                                           December 2023


            Standard Public Key Cryptography (PKC) Test Keys

Abstract

   This document provides a set of standard Public Key Cryptography
   (PKC) test keys that may be used wherever pre-generated keys and
   associated operations like digital signatures are required.  Like the
   European Institute for Computer Antivirus Research (EICAR) virus test
   and the Generic Test for Unsolicited Bulk Email (GTUBE) spam test
   files, these publicly known test keys can be detected and recognised
   by applications consuming them as being purely for testing purposes
   without assigning any security properties to them.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Not all documents
   approved by the IESG are candidates for any level of Internet
   Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc9500.

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Table of Contents

   1.  Introduction
   2.  Publicly Known Test Keys
     2.1.  RSA Keys
     2.2.  DLP Keys
     2.3.  ECDLP Keys
   3.  IANA Considerations
   4.  Security Considerations
   Authors' Addresses

1.  Introduction

   The widespread use of public key cryptosystems on the Internet has
   led to a proliferation of publicly known but not necessarily
   acknowledged keys that are used for testing purposes or that ship
   preconfigured in applications.  These keys provide no security, but
   since there's no record of them, relying parties are often unaware
   that they provide no security.  In order to address this issue, this
   document provides a set of standard public test keys that may be used
   wherever a preconfigured or sample key is required and, by extension,
   also in situations where such keys may be used, such as when testing
   digitally signed data.  Their purpose corresponds roughly to that of
   the European Institute for Computer Antivirus Research (EICAR) test
   file, a non-virus used as a test file for antivirus products, and the
   Generic Test for Unsolicited Bulk Email (GTUBE) file, a similar file
   used with spam-detection products.

   The keys provided cover three major algorithm families:

   *  RSA

   *  algorithms based on the Discrete Logarithm Problem (DLP), such as
      DSA, Diffie-Hellman (DH), and Elgamal

   *  algorithms based on the Elliptic Curve Discrete Logarithm Problem
      (ECDLP), such as ECDSA and Elliptic Curve Diffie-Hellman (ECDH)

   Although some of the algorithms and key sizes are no longer
   recommended, keys corresponding to those algorithms and key sizes are
   provided in order to accommodate the large installed base of existing
   implementations that use them.

   This document does not try to cover every possible algorithm family
   and type since there are far too many of these and new ones are
   constantly appearing and, in some cases, disappearing.  If similar
   documents are created for further algorithm families, they should
   update this document, and for ease of implementation and use, they
   should maintain compatibility with the format and naming conventions
   used here.

2.  Publicly Known Test Keys

   This section provides the test keys for the algorithm groups in
   various sizes in a C-like notation that may be directly used in
   crypto code written in C-like languages such as C, C++, Java,
   JavaScript, Go, Swift, and Rust, covering the majority of languages
   likely to be used to implement crypto code.

   Alongside the source code format, they are also provided in encoded
   form, specifically the OpenSSL private key format, which many
   applications can process directly.

   Each element of the key is given in a form consisting of a count in
   bits (the value from which the nominal key size is taken) followed by
   a byte string containing that key element in big-endian form.  For
   example, the following is a sample key component for the RSA p value,
   where 0xCF is the most significant byte of the RSA p value and 0x03
   is the least significant byte of the value:

       /* p */
       512,
       { 0xCF, 0xDA, 0xF9, 0x99, 0x6F, 0x05, 0x95, 0x84,
         0x09, 0x90, 0xB3, 0xAB, 0x39, 0xB7, 0xDD, 0x1D,
         [...]
         0xE1, 0x2C, 0x0D, 0xF7, 0x30, 0xE2, 0xB8, 0x09,
         0x73, 0x50, 0x28, 0xF6, 0x55, 0x85, 0x57, 0x03 },

   In addition to the key data, each key is given a recommended name for
   use in source code as a means of providing a standard reference for
   each one.

2.1.  RSA Keys

   The following publicly known test keys may be used for RSA.

   RSA-1024 key "testRSA1024":

           /* n */
           1024,
           { 0xB0, 0xD1, 0x83, 0x52, 0xA8, 0x8F, 0x53, 0xD5,
             0x51, 0x6F, 0x46, 0xC2, 0x0E, 0x7A, 0x36, 0x7D,
             0x7D, 0xE8, 0x8A, 0xCF, 0x54, 0xA0, 0x19, 0xF6,
             0xDE, 0xF5, 0x7A, 0xB9, 0xB4, 0x4C, 0xED, 0xDB,
             0x22, 0x42, 0xB1, 0xBC, 0xA0, 0xFB, 0x1B, 0x5C,
             0xB8, 0x2B, 0x30, 0x36, 0x17, 0x6A, 0x63, 0x90,
             0x35, 0x64, 0xDE, 0xC6, 0xEB, 0x41, 0xDB, 0x2F,
             0x8F, 0xC7, 0x87, 0xF4, 0xE5, 0x2E, 0x11, 0x49,
             0xE3, 0x33, 0x47, 0x57, 0x29, 0x73, 0xF6, 0x60,
             0xC3, 0xC7, 0x7C, 0xA9, 0xE0, 0x82, 0x1C, 0x2B,
             0x69, 0x5B, 0xE7, 0xAE, 0x9D, 0x7D, 0x30, 0xF4,
             0x07, 0x91, 0x10, 0xF4, 0x8A, 0xAE, 0x6F, 0x8B,
             0x70, 0x2D, 0x47, 0x4B, 0x29, 0x00, 0x81, 0x7F,
             0x28, 0x66, 0x24, 0x9B, 0xEC, 0x12, 0xA2, 0xB1,
             0x9B, 0x82, 0x78, 0x41, 0x68, 0x08, 0xF8, 0x1A,
             0xE1, 0xFC, 0xF9, 0xB7, 0x77, 0x8A, 0x62, 0x3F },
           /* e */
           17,
           { 0x01, 0x00, 0x01 },
           /* d */
           1023,
           { 0x48, 0x2E, 0x9F, 0x8F, 0xA4, 0xE4, 0x2D, 0xF3,
             0x0D, 0x75, 0x81, 0xCB, 0x42, 0xA1, 0xBD, 0x90,
             0xE9, 0x4F, 0x7F, 0x2B, 0x38, 0x7E, 0xCB, 0x5A,
             0xAE, 0x96, 0x43, 0xED, 0x7F, 0x9F, 0x50, 0x12,
             0x7F, 0x1F, 0xFE, 0xF2, 0xE4, 0x3C, 0xDE, 0x64,
             0xB1, 0x82, 0x60, 0x02, 0x14, 0xF9, 0x07, 0x80,
             0x1D, 0x6B, 0xFA, 0x4D, 0xF6, 0x48, 0x42, 0x34,
             0x5E, 0x5B, 0xB4, 0x32, 0xD3, 0x44, 0x45, 0x25,
             0xD8, 0x30, 0x16, 0x54, 0xC5, 0x44, 0x2B, 0x0A,
             0x5E, 0x11, 0xB9, 0xC7, 0xE2, 0x01, 0xFA, 0x32,
             0xF4, 0x1A, 0xBA, 0xF4, 0xF0, 0xA6, 0xE0, 0x3C,
             0xF0, 0xE0, 0xCB, 0x82, 0x66, 0xC6, 0x2A, 0xD1,
             0x1D, 0x95, 0x6D, 0x53, 0xC9, 0x46, 0x6E, 0x48,
             0x99, 0x5F, 0xEA, 0x26, 0x0C, 0x85, 0x36, 0xF0,
             0x41, 0xCB, 0x35, 0x62, 0xFA, 0xAC, 0x51, 0x1C,
             0x4D, 0x66, 0xA8, 0xFE, 0xD1, 0x11, 0xB2, 0x91 },
           /* p */
           512,
           { 0xE9, 0xD8, 0x6E, 0x4D, 0xC3, 0x4A, 0x98, 0x5A,
             0x7E, 0xC7, 0x5A, 0x6F, 0x54, 0xA7, 0x5C, 0xE4,
             0x51, 0x39, 0xE4, 0x52, 0x40, 0xB3, 0x86, 0xAB,
             0x71, 0x1D, 0xB7, 0x91, 0xBC, 0xD9, 0x87, 0x18,
             0xA1, 0x3B, 0xAF, 0x21, 0x8C, 0x24, 0x49, 0x36,
             0x46, 0x68, 0x07, 0x56, 0xCB, 0x50, 0xA6, 0xCB,
             0xEE, 0x15, 0x8E, 0x25, 0x21, 0x44, 0x99, 0x12,
             0x30, 0x1C, 0x0D, 0x41, 0x49, 0x11, 0x18, 0x45 },
           /* q */
           512,
           { 0xC1, 0x91, 0xFA, 0x3B, 0x55, 0x0B, 0x39, 0x1A,
             0x7C, 0xB0, 0x72, 0x83, 0x76, 0x27, 0x72, 0x95,
             0xE6, 0x1C, 0x65, 0x4F, 0x0B, 0xEF, 0x2F, 0x58,
             0xDC, 0xE5, 0xC9, 0x62, 0xA1, 0x0B, 0x7D, 0xD7,
             0x5F, 0x06, 0x01, 0x54, 0x65, 0xE5, 0x50, 0x76,
             0xE4, 0x66, 0x26, 0x3E, 0xEB, 0xCA, 0xED, 0x20,
             0xD2, 0xEB, 0xAB, 0x39, 0x31, 0x3E, 0x8B, 0xC5,
             0x67, 0x32, 0x0F, 0xE8, 0xB2, 0xDC, 0x62, 0xB3 },
           /* u */
           512,
           { 0xB9, 0x9D, 0x7F, 0x8F, 0x4D, 0x4D, 0x45, 0x5F,
             0x1F, 0xBA, 0x46, 0x2D, 0x99, 0x0A, 0x2E, 0x84,
             0x8C, 0x42, 0x8C, 0x1E, 0xBE, 0xE0, 0x1D, 0xC0,
             0x01, 0x84, 0xC8, 0xA7, 0x65, 0x83, 0xAD, 0x37,
             0x9F, 0x69, 0xAD, 0xAF, 0x54, 0x75, 0x54, 0x30,
             0xF6, 0x3C, 0x42, 0x53, 0xD1, 0xBB, 0x78, 0xCC,
             0x9B, 0xD2, 0x32, 0x64, 0x34, 0x00, 0x80, 0xB8,
             0x4C, 0x1A, 0x91, 0x7D, 0xE0, 0x8B, 0x6E, 0xDB },
           /* exponent1 */
           512,
           { 0xE7, 0x3A, 0xE0, 0x37, 0x7C, 0xB8, 0xB2, 0x56,
             0x29, 0xAE, 0xAE, 0xBA, 0x0F, 0x97, 0x3E, 0xBF,
             0x75, 0xA2, 0x2D, 0x27, 0x38, 0x5B, 0x4C, 0xFB,
             0x11, 0xEB, 0x34, 0xAD, 0xA3, 0x73, 0xE5, 0xA6,
             0x71, 0x28, 0x37, 0x50, 0x90, 0xE7, 0x00, 0x8D,
             0xEE, 0xA8, 0xC7, 0x39, 0x07, 0xEA, 0x44, 0x44,
             0xBA, 0xB4, 0x0D, 0xCE, 0xA1, 0x4A, 0xD7, 0xA1,
             0xA8, 0x78, 0xD4, 0x92, 0x8D, 0xD1, 0x9D, 0x91 },
           /* exponent2 */
           511,
           { 0x41, 0x99, 0x79, 0x16, 0x16, 0x72, 0x21, 0x3E,
             0x0A, 0xB7, 0xB9, 0x77, 0x37, 0xD9, 0x92, 0x89,
             0x9E, 0x5C, 0x4D, 0x31, 0x06, 0xB8, 0x5E, 0x71,
             0x5D, 0x1B, 0x3A, 0xAE, 0x84, 0x29, 0x62, 0xD2,
             0x54, 0x4F, 0xB2, 0xAF, 0xA9, 0x80, 0x97, 0x4E,
             0x53, 0x85, 0x12, 0xBD, 0x0C, 0x27, 0xCF, 0x48,
             0xEA, 0x72, 0x17, 0xAA, 0xE0, 0x37, 0x74, 0x22,
             0xC8, 0x20, 0x3D, 0x27, 0xFD, 0x45, 0x96, 0xE5 }

   RSA-1024 key in encoded form:

   -----BEGIN RSA PRIVATE KEY-----
   MIICXQIBAAKBgQCw0YNSqI9T1VFvRsIOejZ9feiKz1SgGfbe9Xq5tEzt2yJCsbyg
   +xtcuCswNhdqY5A1ZN7G60HbL4/Hh/TlLhFJ4zNHVylz9mDDx3yp4IIcK2lb566d
   fTD0B5EQ9Iqub4twLUdLKQCBfyhmJJvsEqKxm4J4QWgI+Brh/Pm3d4piPwIDAQAB
   AoGASC6fj6TkLfMNdYHLQqG9kOlPfys4fstarpZD7X+fUBJ/H/7y5DzeZLGCYAIU
   +QeAHWv6TfZIQjReW7Qy00RFJdgwFlTFRCsKXhG5x+IB+jL0Grr08KbgPPDgy4Jm
   xirRHZVtU8lGbkiZX+omDIU28EHLNWL6rFEcTWao/tERspECQQDp2G5Nw0qYWn7H
   Wm9Up1zkUTnkUkCzhqtxHbeRvNmHGKE7ryGMJEk2RmgHVstQpsvuFY4lIUSZEjAc
   DUFJERhFAkEAwZH6O1ULORp8sHKDdidyleYcZU8L7y9Y3OXJYqELfddfBgFUZeVQ
   duRmJj7ryu0g0uurOTE+i8VnMg/ostxiswJBAOc64Dd8uLJWKa6uug+XPr91oi0n
   OFtM+xHrNK2jc+WmcSg3UJDnAI3uqMc5B+pERLq0Dc6hStehqHjUko3RnZECQEGZ
   eRYWciE+Cre5dzfZkomeXE0xBrhecV0bOq6EKWLSVE+yr6mAl05ThRK9DCfPSOpy
   F6rgN3QiyCA9J/1FluUCQQC5nX+PTU1FXx+6Ri2ZCi6EjEKMHr7gHcABhMinZYOt
   N59pra9UdVQw9jxCU9G7eMyb0jJkNACAuEwakX3gi27b
   -----END RSA PRIVATE KEY-----

   RSA-2048 key "testRSA2048":

           /* n */
           2048,
           { 0xB0, 0xF9, 0xE8, 0x19, 0x43, 0xA7, 0xAE, 0x98,
             0x92, 0xAA, 0xDE, 0x17, 0xCA, 0x7C, 0x40, 0xF8,
             0x74, 0x4F, 0xED, 0x2F, 0x81, 0x48, 0xE6, 0xC8,
             0xEA, 0xA2, 0x7B, 0x7D, 0x00, 0x15, 0x48, 0xFB,
             0x51, 0x92, 0xAB, 0x28, 0xB5, 0x6C, 0x50, 0x60,
             0xB1, 0x18, 0xCC, 0xD1, 0x31, 0xE5, 0x94, 0x87,
             0x4C, 0x6C, 0xA9, 0x89, 0xB5, 0x6C, 0x27, 0x29,
             0x6F, 0x09, 0xFB, 0x93, 0xA0, 0x34, 0xDF, 0x32,
             0xE9, 0x7C, 0x6F, 0xF0, 0x99, 0x8C, 0xFD, 0x8E,
             0x6F, 0x42, 0xDD, 0xA5, 0x8A, 0xCD, 0x1F, 0xA9,
             0x79, 0x86, 0xF1, 0x44, 0xF3, 0xD1, 0x54, 0xD6,
             0x76, 0x50, 0x17, 0x5E, 0x68, 0x54, 0xB3, 0xA9,
             0x52, 0x00, 0x3B, 0xC0, 0x68, 0x87, 0xB8, 0x45,
             0x5A, 0xC2, 0xB1, 0x9F, 0x7B, 0x2F, 0x76, 0x50,
             0x4E, 0xBC, 0x98, 0xEC, 0x94, 0x55, 0x71, 0xB0,
             0x78, 0x92, 0x15, 0x0D, 0xDC, 0x6A, 0x74, 0xCA,
             0x0F, 0xBC, 0xD3, 0x54, 0x97, 0xCE, 0x81, 0x53,
             0x4D, 0xAF, 0x94, 0x18, 0x84, 0x4B, 0x13, 0xAE,
             0xA3, 0x1F, 0x9D, 0x5A, 0x6B, 0x95, 0x57, 0xBB,
             0xDF, 0x61, 0x9E, 0xFD, 0x4E, 0x88, 0x7F, 0x2D,
             0x42, 0xB8, 0xDD, 0x8B, 0xC9, 0x87, 0xEA, 0xE1,
             0xBF, 0x89, 0xCA, 0xB8, 0x5E, 0xE2, 0x1E, 0x35,
             0x63, 0x05, 0xDF, 0x6C, 0x07, 0xA8, 0x83, 0x8E,
             0x3E, 0xF4, 0x1C, 0x59, 0x5D, 0xCC, 0xE4, 0x3D,
             0xAF, 0xC4, 0x91, 0x23, 0xEF, 0x4D, 0x8A, 0xBB,
             0xA9, 0x3D, 0x39, 0x05, 0xE4, 0x02, 0x8D, 0x7B,
             0xA9, 0x14, 0x84, 0xA2, 0x75, 0x96, 0xE0, 0x7B,
             0x4B, 0x6E, 0xD9, 0x92, 0xF0, 0x77, 0xB5, 0x24,
             0xD3, 0xDC, 0xFE, 0x7D, 0xDD, 0x55, 0x49, 0xBE,
             0x7C, 0xCE, 0x8D, 0xA0, 0x35, 0xCF, 0xA0, 0xB3,
             0xFB, 0x8F, 0x9E, 0x46, 0xF7, 0x32, 0xB2, 0xA8,
             0x6B, 0x46, 0x01, 0x65, 0xC0, 0x8F, 0x53, 0x13 },
           /* e */
           17,
           { 0x01, 0x00, 0x01 },
           /* d */
           2047,
           { 0x41, 0x18, 0x8B, 0x20, 0xCF, 0xDB, 0xDB, 0xC2,
             0xCF, 0x1F, 0xFE, 0x75, 0x2D, 0xCB, 0xAA, 0x72,
             0x39, 0x06, 0x35, 0x2E, 0x26, 0x15, 0xD4, 0x9D,
             0xCE, 0x80, 0x59, 0x7F, 0xCF, 0x0A, 0x05, 0x40,
             0x3B, 0xEF, 0x00, 0xFA, 0x06, 0x51, 0x82, 0xF7,
             0x2D, 0xEC, 0xFB, 0x59, 0x6F, 0x4B, 0x0C, 0xE8,
             0xFF, 0x59, 0x70, 0xBA, 0xF0, 0x7A, 0x89, 0xA5,
             0x19, 0xEC, 0xC8, 0x16, 0xB2, 0xF4, 0xFF, 0xAC,
             0x50, 0x69, 0xAF, 0x1B, 0x06, 0xBF, 0xEF, 0x7B,
             0xF6, 0xBC, 0xD7, 0x9E, 0x4E, 0x81, 0xC8, 0xC5,
             0xA3, 0xA7, 0xD9, 0x13, 0x0D, 0xC3, 0xCF, 0xBA,
             0xDA, 0xE5, 0xF6, 0xD2, 0x88, 0xF9, 0xAE, 0xE3,
             0xF6, 0xFF, 0x92, 0xFA, 0xE0, 0xF8, 0x1A, 0xF5,
             0x97, 0xBE, 0xC9, 0x6A, 0xE9, 0xFA, 0xB9, 0x40,
             0x2C, 0xD5, 0xFE, 0x41, 0xF7, 0x05, 0xBE, 0xBD,
             0xB4, 0x7B, 0xB7, 0x36, 0xD3, 0xFE, 0x6C, 0x5A,
             0x51, 0xE0, 0xE2, 0x07, 0x32, 0xA9, 0x7B, 0x5E,
             0x46, 0xC1, 0xCB, 0xDB, 0x26, 0xD7, 0x48, 0x54,
             0xC6, 0xB6, 0x60, 0x4A, 0xED, 0x46, 0x37, 0x35,
             0xFF, 0x90, 0x76, 0x04, 0x65, 0x57, 0xCA, 0xF9,
             0x49, 0xBF, 0x44, 0x88, 0x95, 0xC2, 0x04, 0x32,
             0xC1, 0xE0, 0x9C, 0x01, 0x4E, 0xA7, 0x56, 0x60,
             0x43, 0x4F, 0x1A, 0x0F, 0x3B, 0xE2, 0x94, 0xBA,
             0xBC, 0x5D, 0x53, 0x0E, 0x6A, 0x10, 0x21, 0x3F,
             0x53, 0xB6, 0x03, 0x75, 0xFC, 0x84, 0xA7, 0x57,
             0x3F, 0x2A, 0xF1, 0x21, 0x55, 0x84, 0xF5, 0xB4,
             0xBD, 0xA6, 0xD4, 0xE8, 0xF9, 0xE1, 0x7A, 0x78,
             0xD9, 0x7E, 0x77, 0xB8, 0x6D, 0xA4, 0xA1, 0x84,
             0x64, 0x75, 0x31, 0x8A, 0x7A, 0x10, 0xA5, 0x61,
             0x01, 0x4E, 0xFF, 0xA2, 0x3A, 0x81, 0xEC, 0x56,
             0xE9, 0xE4, 0x10, 0x9D, 0xEF, 0x8C, 0xB3, 0xF7,
             0x97, 0x22, 0x3F, 0x7D, 0x8D, 0x0D, 0x43, 0x51 },
           /* p */
           1024,
           { 0xDD, 0x10, 0x57, 0x02, 0x38, 0x2F, 0x23, 0x2B,
             0x36, 0x81, 0xF5, 0x37, 0x91, 0xE2, 0x26, 0x17,
             0xC7, 0xBF, 0x4E, 0x9A, 0xCB, 0x81, 0xED, 0x48,
             0xDA, 0xF6, 0xD6, 0x99, 0x5D, 0xA3, 0xEA, 0xB6,
             0x42, 0x83, 0x9A, 0xFF, 0x01, 0x2D, 0x2E, 0xA6,
             0x28, 0xB9, 0x0A, 0xF2, 0x79, 0xFD, 0x3E, 0x6F,
             0x7C, 0x93, 0xCD, 0x80, 0xF0, 0x72, 0xF0, 0x1F,
             0xF2, 0x44, 0x3B, 0x3E, 0xE8, 0xF2, 0x4E, 0xD4,
             0x69, 0xA7, 0x96, 0x13, 0xA4, 0x1B, 0xD2, 0x40,
             0x20, 0xF9, 0x2F, 0xD1, 0x10, 0x59, 0xBD, 0x1D,
             0x0F, 0x30, 0x1B, 0x5B, 0xA7, 0xA9, 0xD3, 0x63,
             0x7C, 0xA8, 0xD6, 0x5C, 0x1A, 0x98, 0x15, 0x41,
             0x7D, 0x8E, 0xAB, 0x73, 0x4B, 0x0B, 0x4F, 0x3A,
             0x2C, 0x66, 0x1D, 0x9A, 0x1A, 0x82, 0xF3, 0xAC,
             0x73, 0x4C, 0x40, 0x53, 0x06, 0x69, 0xAB, 0x8E,
             0x47, 0x30, 0x45, 0xA5, 0x8E, 0x65, 0x53, 0x9D },
           /* q */
           1024,
           { 0xCC, 0xF1, 0xE5, 0xBB, 0x90, 0xC8, 0xE9, 0x78,
             0x1E, 0xA7, 0x5B, 0xEB, 0xF1, 0x0B, 0xC2, 0x52,
             0xE1, 0x1E, 0xB0, 0x23, 0xA0, 0x26, 0x0F, 0x18,
             0x87, 0x55, 0x2A, 0x56, 0x86, 0x3F, 0x4A, 0x64,
             0x21, 0xE8, 0xC6, 0x00, 0xBF, 0x52, 0x3D, 0x6C,
             0xB1, 0xB0, 0xAD, 0xBD, 0xD6, 0x5B, 0xFE, 0xE4,
             0xA8, 0x8A, 0x03, 0x7E, 0x3D, 0x1A, 0x41, 0x5E,
             0x5B, 0xB9, 0x56, 0x48, 0xDA, 0x5A, 0x0C, 0xA2,
             0x6B, 0x54, 0xF4, 0xA6, 0x39, 0x48, 0x52, 0x2C,
             0x3D, 0x5F, 0x89, 0xB9, 0x4A, 0x72, 0xEF, 0xFF,
             0x95, 0x13, 0x4D, 0x59, 0x40, 0xCE, 0x45, 0x75,
             0x8F, 0x30, 0x89, 0x80, 0x90, 0x89, 0x56, 0x58,
             0x8E, 0xEF, 0x57, 0x5B, 0x3E, 0x4B, 0xC4, 0xC3,
             0x68, 0xCF, 0xE8, 0x13, 0xEE, 0x9C, 0x25, 0x2C,
             0x2B, 0x02, 0xE0, 0xDF, 0x91, 0xF1, 0xAA, 0x01,
             0x93, 0x8D, 0x38, 0x68, 0x5D, 0x60, 0xBA, 0x6F },
           /* u */
           1020,
           { 0x0A, 0x81, 0xD8, 0xA6, 0x18, 0x31, 0x4A, 0x80,
             0x3A, 0xF6, 0x1C, 0x06, 0x71, 0x1F, 0x2C, 0x39,
             0xB2, 0x66, 0xFF, 0x41, 0x4D, 0x53, 0x47, 0x6D,
             0x1D, 0xA5, 0x2A, 0x43, 0x18, 0xAA, 0xFE, 0x4B,
             0x96, 0xF0, 0xDA, 0x07, 0x15, 0x5F, 0x8A, 0x51,
             0x34, 0xDA, 0xB8, 0x8E, 0xE2, 0x9E, 0x81, 0x68,
             0x07, 0x6F, 0xCD, 0x78, 0xCA, 0x79, 0x1A, 0xC6,
             0x34, 0x42, 0xA8, 0x1C, 0xD0, 0x69, 0x39, 0x27,
             0xD8, 0x08, 0xE3, 0x35, 0xE8, 0xD8, 0xCB, 0xF2,
             0x12, 0x19, 0x07, 0x50, 0x9A, 0x57, 0x75, 0x9B,
             0x4F, 0x9A, 0x18, 0xFA, 0x3A, 0x7B, 0x33, 0x37,
             0x79, 0xED, 0xDE, 0x7A, 0x45, 0x93, 0x84, 0xF8,
             0x44, 0x4A, 0xDA, 0xEC, 0xFF, 0xEC, 0x95, 0xFD,
             0x55, 0x2B, 0x0C, 0xFC, 0xB6, 0xC7, 0xF6, 0x92,
             0x62, 0x6D, 0xDE, 0x1E, 0xF2, 0x68, 0xA4, 0x0D,
             0x2F, 0x67, 0xB5, 0xC8, 0xAA, 0x38, 0x7F, 0xF7 },
           /* exponent1 */
           1020,
           { 0x09, 0xED, 0x54, 0xEA, 0xED, 0x98, 0xF8, 0x4C,
             0x55, 0x7B, 0x4A, 0x86, 0xBF, 0x4F, 0x57, 0x84,
             0x93, 0xDC, 0xBC, 0x6B, 0xE9, 0x1D, 0xA1, 0x89,
             0x37, 0x04, 0x04, 0xA9, 0x08, 0x72, 0x76, 0xF4,
             0xCE, 0x51, 0xD8, 0xA1, 0x00, 0xED, 0x85, 0x7D,
             0xC2, 0xB0, 0x64, 0x94, 0x74, 0xF3, 0xF1, 0x5C,
             0xD2, 0x4C, 0x54, 0xDB, 0x28, 0x71, 0x10, 0xE5,
             0x6E, 0x5C, 0xB0, 0x08, 0x68, 0x2F, 0x91, 0x68,
             0xAA, 0x81, 0xF3, 0x14, 0x58, 0xB7, 0x43, 0x1E,
             0xCC, 0x1C, 0x44, 0x90, 0x6F, 0xDA, 0x87, 0xCA,
             0x89, 0x47, 0x10, 0xC3, 0x71, 0xE9, 0x07, 0x6C,
             0x1D, 0x49, 0xFB, 0xAE, 0x51, 0x27, 0x69, 0x34,
             0xF2, 0xAD, 0x78, 0x77, 0x89, 0xF4, 0x2D, 0x0F,
             0xA0, 0xB4, 0xC9, 0x39, 0x85, 0x5D, 0x42, 0x12,
             0x09, 0x6F, 0x70, 0x28, 0x0A, 0x4E, 0xAE, 0x7C,
             0x8A, 0x27, 0xD9, 0xC8, 0xD0, 0x77, 0x2E, 0x65 },
           /* exponent2 */
           1024,
           { 0x8C, 0xB6, 0x85, 0x7A, 0x7B, 0xD5, 0x46, 0x5F,
             0x80, 0x04, 0x7E, 0x9B, 0x87, 0xBC, 0x00, 0x27,
             0x31, 0x84, 0x05, 0x81, 0xE0, 0x62, 0x61, 0x39,
             0x01, 0x2A, 0x5B, 0x50, 0x5F, 0x0A, 0x33, 0x84,
             0x7E, 0xB7, 0xB8, 0xC3, 0x28, 0x99, 0x49, 0xAD,
             0x48, 0x6F, 0x3B, 0x4B, 0x3D, 0x53, 0x9A, 0xB5,
             0xDA, 0x76, 0x30, 0x21, 0xCB, 0xC8, 0x2C, 0x1B,
             0xA2, 0x34, 0xA5, 0x66, 0x8D, 0xED, 0x08, 0x01,
             0xB8, 0x59, 0xF3, 0x43, 0xF1, 0xCE, 0x93, 0x04,
             0xE6, 0xFA, 0xA2, 0xB0, 0x02, 0xCA, 0xD9, 0xB7,
             0x8C, 0xDE, 0x5C, 0xDC, 0x2C, 0x1F, 0xB4, 0x17,
             0x1C, 0x42, 0x42, 0x16, 0x70, 0xA6, 0xAB, 0x0F,
             0x50, 0xCC, 0x4A, 0x19, 0x4E, 0xB3, 0x6D, 0x1C,
             0x91, 0xE9, 0x35, 0xBA, 0x01, 0xB9, 0x59, 0xD8,
             0x72, 0x8B, 0x9E, 0x64, 0x42, 0x6B, 0x3F, 0xC3,
             0xA7, 0x50, 0x6D, 0xEB, 0x52, 0x39, 0xA8, 0xA7 }

   RSA-2048 key in encoded form:

   -----BEGIN RSA PRIVATE KEY-----
   MIIEowIBAAKCAQEAsPnoGUOnrpiSqt4XynxA+HRP7S+BSObI6qJ7fQAVSPtRkqso
   tWxQYLEYzNEx5ZSHTGypibVsJylvCfuToDTfMul8b/CZjP2Ob0LdpYrNH6l5hvFE
   89FU1nZQF15oVLOpUgA7wGiHuEVawrGfey92UE68mOyUVXGweJIVDdxqdMoPvNNU
   l86BU02vlBiESxOuox+dWmuVV7vfYZ79Toh/LUK43YvJh+rhv4nKuF7iHjVjBd9s
   B6iDjj70HFldzOQ9r8SRI+9NirupPTkF5AKNe6kUhKJ1luB7S27ZkvB3tSTT3P59
   3VVJvnzOjaA1z6Cz+4+eRvcysqhrRgFlwI9TEwIDAQABAoIBAEEYiyDP29vCzx/+
   dS3LqnI5BjUuJhXUnc6AWX/PCgVAO+8A+gZRgvct7PtZb0sM6P9ZcLrweomlGezI
   FrL0/6xQaa8bBr/ve/a8155OgcjFo6fZEw3Dz7ra5fbSiPmu4/b/kvrg+Br1l77J
   aun6uUAs1f5B9wW+vbR7tzbT/mxaUeDiBzKpe15GwcvbJtdIVMa2YErtRjc1/5B2
   BGVXyvlJv0SIlcIEMsHgnAFOp1ZgQ08aDzvilLq8XVMOahAhP1O2A3X8hKdXPyrx
   IVWE9bS9ptTo+eF6eNl+d7htpKGEZHUxinoQpWEBTv+iOoHsVunkEJ3vjLP3lyI/
   fY0NQ1ECgYEA3RBXAjgvIys2gfU3keImF8e/TprLge1I2vbWmV2j6rZCg5r/AS0u
   pii5CvJ5/T5vfJPNgPBy8B/yRDs+6PJO1GmnlhOkG9JAIPkv0RBZvR0PMBtbp6nT
   Y3yo1lwamBVBfY6rc0sLTzosZh2aGoLzrHNMQFMGaauORzBFpY5lU50CgYEAzPHl
   u5DI6Xgep1vr8QvCUuEesCOgJg8Yh1UqVoY/SmQh6MYAv1I9bLGwrb3WW/7kqIoD
   fj0aQV5buVZI2loMomtU9KY5SFIsPV+JuUpy7/+VE01ZQM5FdY8wiYCQiVZYju9X
   Wz5LxMNoz+gT7pwlLCsC4N+R8aoBk404aF1gum8CgYAJ7VTq7Zj4TFV7Soa/T1eE
   k9y8a+kdoYk3BASpCHJ29M5R2KEA7YV9wrBklHTz8VzSTFTbKHEQ5W5csAhoL5Fo
   qoHzFFi3Qx7MHESQb9qHyolHEMNx6QdsHUn7rlEnaTTyrXh3ifQtD6C0yTmFXUIS
   CW9wKApOrnyKJ9nI0HcuZQKBgQCMtoV6e9VGX4AEfpuHvAAnMYQFgeBiYTkBKltQ
   XwozhH63uMMomUmtSG87Sz1TmrXadjAhy8gsG6I0pWaN7QgBuFnzQ/HOkwTm+qKw
   AsrZt4zeXNwsH7QXHEJCFnCmqw9QzEoZTrNtHJHpNboBuVnYcoueZEJrP8OnUG3r
   UjmopwKBgAqB2KYYMUqAOvYcBnEfLDmyZv9BTVNHbR2lKkMYqv5LlvDaBxVfilE0
   2riO4p6BaAdvzXjKeRrGNEKoHNBpOSfYCOM16NjL8hIZB1CaV3WbT5oY+jp7Mzd5
   7d56RZOE+ERK2uz/7JX9VSsM/LbH9pJibd4e8mikDS9ntciqOH/3
   -----END RSA PRIVATE KEY-----

   RSA-4096 key "testRSA4096":

           /* n */
           4096,
           { 0xB3, 0x8B, 0x49, 0x60, 0xE6, 0x3B, 0xE6, 0xA8,
             0xDB, 0xA8, 0x9A, 0x82, 0x97, 0x8E, 0xF1, 0xF6,
             0x32, 0x44, 0xE5, 0x57, 0x7D, 0x8C, 0xF5, 0x86,
             0x16, 0xD5, 0xCA, 0x57, 0x59, 0xD4, 0x9C, 0xC8,
             0xD9, 0x36, 0xC3, 0x38, 0xAA, 0x3C, 0xB9, 0xB1,
             0x11, 0xC1, 0x49, 0x7E, 0x5B, 0x51, 0xAF, 0x69,
             0x2F, 0x26, 0x11, 0xE6, 0x89, 0xF7, 0x67, 0x54,
             0x80, 0xC0, 0xB0, 0xF4, 0xC3, 0x65, 0x4F, 0x43,
             0xAF, 0x85, 0xFE, 0x8C, 0x8A, 0xD7, 0x34, 0xE0,
             0x42, 0xA8, 0xAD, 0xA0, 0x5F, 0xD7, 0x65, 0x08,
             0xE0, 0x0B, 0xA0, 0xF7, 0x56, 0xC3, 0x44, 0x3B,
             0xBE, 0x83, 0x3E, 0xA7, 0xD1, 0x00, 0xD4, 0xFB,
             0x36, 0x7E, 0xEB, 0xD6, 0x0B, 0xDB, 0x64, 0x86,
             0x77, 0xFC, 0x7D, 0xEB, 0x94, 0x24, 0x4D, 0xAD,
             0x1A, 0xF8, 0xEE, 0xD1, 0xC6, 0x58, 0x12, 0xC0,
             0x3E, 0x7C, 0x73, 0xF7, 0xF3, 0x58, 0xE9, 0x41,
             0xBC, 0x66, 0x45, 0x8F, 0xF7, 0xBB, 0x97, 0xA4,
             0x9A, 0x98, 0xA1, 0x18, 0x07, 0xE0, 0x2C, 0x1A,
             0x3B, 0x9A, 0xD3, 0x3A, 0x57, 0x3A, 0xE1, 0x80,
             0xE1, 0xFF, 0x43, 0x2A, 0xE5, 0x58, 0x0C, 0xC9,
             0xCA, 0xBF, 0xAB, 0x60, 0x2F, 0x32, 0x5B, 0xCD,
             0xA0, 0x97, 0xE8, 0x7B, 0xC7, 0xA6, 0xD7, 0x4E,
             0x34, 0xA8, 0x7D, 0x60, 0x8A, 0x43, 0xFE, 0xB2,
             0xE4, 0xFF, 0xF1, 0xF4, 0xB8, 0xE7, 0x68, 0x6A,
             0x98, 0x47, 0x5D, 0xB5, 0x1A, 0x6E, 0xBD, 0x08,
             0x17, 0x2A, 0x57, 0x41, 0x77, 0x49, 0x24, 0x8B,
             0x21, 0x55, 0xC8, 0xB9, 0x06, 0xE0, 0xD5, 0x40,
             0xE8, 0xCB, 0x28, 0xF4, 0xC0, 0x0A, 0xDC, 0x9F,
             0xE4, 0x75, 0x8A, 0x1A, 0xC3, 0x64, 0xAB, 0x39,
             0xE4, 0xE1, 0x55, 0x28, 0x98, 0x54, 0x44, 0x15,
             0x3F, 0xEE, 0xC6, 0xAD, 0x4C, 0x53, 0x48, 0xB2,
             0xE3, 0x8F, 0xF5, 0x50, 0xF5, 0xFA, 0x58, 0x33,
             0x97, 0x93, 0x37, 0x30, 0xC8, 0x08, 0x81, 0xBF,
             0x11, 0xEE, 0xE8, 0xFE, 0x38, 0x6D, 0x5B, 0x51,
             0x28, 0x49, 0xA9, 0x83, 0x99, 0x43, 0xAB, 0xF3,
             0xD9, 0x72, 0x20, 0x76, 0x97, 0xB8, 0xEC, 0x24,
             0x11, 0xA2, 0x61, 0x9D, 0x55, 0xCA, 0x04, 0x23,
             0x3C, 0x5A, 0x2C, 0xED, 0xC6, 0xF2, 0x86, 0xD8,
             0x29, 0xD0, 0xE8, 0x37, 0x20, 0x7B, 0x76, 0x52,
             0x9A, 0xA2, 0x44, 0x87, 0x21, 0x26, 0x8D, 0xC0,
             0x15, 0x0B, 0xB7, 0xB0, 0x7E, 0x73, 0x31, 0x3A,
             0x71, 0x3E, 0x58, 0x95, 0xBA, 0xAF, 0x3A, 0xDF,
             0xFA, 0x60, 0x39, 0x58, 0xC5, 0x67, 0xF8, 0x5C,
             0xF2, 0x5B, 0x1D, 0x80, 0xA2, 0x77, 0x56, 0xA3,
             0x0D, 0x1A, 0x50, 0xA1, 0xE4, 0x69, 0x8E, 0xDA,
             0x9A, 0x12, 0x2B, 0xB0, 0xAA, 0x7A, 0x60, 0xF7,
             0xCD, 0x22, 0x6C, 0xB1, 0x16, 0x5C, 0xFC, 0xF9,
             0xCA, 0x83, 0x0A, 0x60, 0x6C, 0xC0, 0xFB, 0x14,
             0x87, 0xF2, 0x49, 0xE5, 0xE0, 0xC7, 0x1C, 0x88,
             0x62, 0x6C, 0x57, 0x12, 0x80, 0x81, 0xDE, 0x76,
             0xC1, 0x23, 0x84, 0xB6, 0xD4, 0x48, 0xB6, 0x7F,
             0x0E, 0x71, 0x23, 0xAE, 0xEF, 0x74, 0xA8, 0x85,
             0x96, 0x03, 0x74, 0x75, 0x54, 0x83, 0xF2, 0x90,
             0xA7, 0xDE, 0x66, 0x46, 0x5E, 0x22, 0x7B, 0x2B,
             0x17, 0x31, 0x8F, 0x8A, 0x49, 0x05, 0x2B, 0x01,
             0x45, 0xFB, 0xA2, 0x83, 0x77, 0x2B, 0xC2, 0x9A,
             0x5B, 0x58, 0x12, 0xAC, 0xCE, 0xE3, 0xAB, 0x62,
             0x81, 0x70, 0x19, 0xE5, 0x48, 0x07, 0xF2, 0x88,
             0x97, 0x12, 0xB7, 0xB8, 0xF3, 0x03, 0xBA, 0x5F,
             0xE1, 0x47, 0xF9, 0xC2, 0xF3, 0x43, 0x4A, 0xB7,
             0x03, 0xC1, 0xD9, 0x46, 0x73, 0x43, 0x82, 0xA0,
             0xA3, 0x53, 0xF4, 0xE0, 0xCB, 0xBE, 0xA2, 0x6A,
             0x4B, 0xBF, 0x21, 0xCE, 0x9E, 0xB5, 0xE7, 0x9D,
             0x47, 0x57, 0xD7, 0xDE, 0x02, 0x7F, 0x20, 0xE5 },
           /* e */
           17,
           { 0x01, 0x00, 0x01 },
           /* d */
           4095,
           { 0x6A, 0xD1, 0xB0, 0xBB, 0x7C, 0xDF, 0x20, 0x91,
             0x4F, 0xF6, 0x94, 0xCE, 0xA3, 0x7B, 0x01, 0x4B,
             0xD7, 0x86, 0x93, 0xE8, 0x24, 0xA3, 0x4B, 0xA4,
             0x16, 0x4B, 0xE5, 0xD1, 0x68, 0x79, 0x8D, 0x3A,
             0x15, 0xB9, 0x76, 0x16, 0x6D, 0x7A, 0x29, 0x84,
             0x46, 0xAA, 0xF7, 0x9D, 0xBC, 0x98, 0xF1, 0xC2,
             0xA3, 0xB1, 0x83, 0xAE, 0xE4, 0x60, 0x94, 0x52,
             0x7B, 0x33, 0xA9, 0x54, 0x46, 0x38, 0x2D, 0x1B,
             0x78, 0xFF, 0x40, 0x7D, 0xBF, 0x50, 0xE0, 0x7D,
             0x98, 0x4B, 0x20, 0xD9, 0xAC, 0x8B, 0xCA, 0xE9,
             0xA7, 0xDA, 0x63, 0x4F, 0x24, 0x88, 0x92, 0x3C,
             0xF5, 0x50, 0xC2, 0x63, 0x37, 0x7E, 0xC6, 0x38,
             0x1B, 0xA9, 0x11, 0x88, 0xCC, 0x8F, 0x1F, 0xD4,
             0xBC, 0xE8, 0x34, 0xC6, 0x86, 0xE1, 0xBE, 0x71,
             0x01, 0xFE, 0x1E, 0xA0, 0x21, 0xE0, 0x5E, 0x6F,
             0x8F, 0xFD, 0x9D, 0x45, 0x64, 0xBB, 0x7E, 0x33,
             0x84, 0xF2, 0x57, 0xEA, 0x9A, 0x9A, 0x3A, 0x53,
             0x4D, 0x43, 0x07, 0x7C, 0xF3, 0x9A, 0x94, 0xC2,
             0x9A, 0xB9, 0xB7, 0x78, 0x1B, 0x53, 0xC5, 0xBC,
             0x57, 0x38, 0xF6, 0x6E, 0x3B, 0xFA, 0xD1, 0xC8,
             0xF0, 0xDE, 0x6E, 0x08, 0x90, 0xAB, 0xE6, 0x60,
             0x85, 0x6E, 0x3B, 0x7C, 0x01, 0x41, 0xAB, 0x11,
             0x35, 0x55, 0x15, 0x1A, 0xED, 0xC8, 0x1C, 0x6D,
             0xB4, 0xBE, 0xED, 0xE6, 0x0A, 0x68, 0x6B, 0x00,
             0x18, 0x4F, 0x45, 0x5A, 0x2D, 0x3A, 0xBB, 0x2E,
             0x68, 0x11, 0xE1, 0xCD, 0xEA, 0x39, 0x53, 0x0B,
             0x8F, 0xAE, 0xA8, 0xF8, 0x24, 0x36, 0x79, 0xC9,
             0xDF, 0x76, 0x97, 0x8C, 0x5E, 0x01, 0x58, 0x57,
             0xAC, 0xA5, 0x9D, 0x9F, 0xE4, 0xA6, 0x2D, 0x15,
             0x09, 0xAE, 0x62, 0x6A, 0xFF, 0x8E, 0x0A, 0xDF,
             0x95, 0xA4, 0xEB, 0x01, 0x49, 0xCA, 0xB7, 0x12,
             0xEF, 0x3E, 0xC3, 0xD6, 0x02, 0x32, 0x8A, 0x6C,
             0x50, 0x21, 0xBA, 0x1B, 0x35, 0xB8, 0x58, 0x3D,
             0x9A, 0x90, 0x40, 0x55, 0x03, 0xF5, 0xFA, 0x0F,
             0x42, 0x4C, 0x72, 0x86, 0x23, 0xFC, 0x81, 0xD3,
             0xDD, 0x7B, 0xFF, 0x1B, 0xF7, 0x8C, 0x8E, 0x2E,
             0xBD, 0x03, 0xA5, 0x11, 0x2D, 0xEB, 0x65, 0x89,
             0x98, 0x6E, 0x49, 0xBD, 0x30, 0x07, 0x1A, 0xD8,
             0x41, 0xA3, 0xCC, 0xA8, 0x07, 0x6C, 0xCF, 0xC7,
             0x94, 0x63, 0x30, 0xB1, 0xFD, 0x1C, 0x21, 0x2A,
             0xD3, 0xEB, 0xD3, 0x7D, 0x9A, 0x4D, 0x0A, 0x96,
             0x95, 0xB8, 0x16, 0x8A, 0x08, 0x89, 0x32, 0x7D,
             0x52, 0x6F, 0x16, 0xD1, 0x56, 0x37, 0xFA, 0x9D,
             0xBF, 0x04, 0xB0, 0xB8, 0x3D, 0xD8, 0xB5, 0xC4,
             0x05, 0x2D, 0xC5, 0x38, 0xB6, 0xCA, 0xE9, 0xC9,
             0x2E, 0xC9, 0x70, 0x10, 0x7A, 0x2F, 0x1E, 0xE4,
             0xD4, 0x7A, 0x65, 0xCC, 0xA5, 0xB9, 0x59, 0x6E,
             0x42, 0x74, 0x91, 0x9B, 0xE7, 0xD1, 0xEC, 0x90,
             0xE4, 0x50, 0xFE, 0x58, 0x58, 0xDC, 0x2E, 0x01,
             0xE8, 0x4E, 0xBD, 0x92, 0x07, 0xD8, 0xEA, 0x20,
             0xFA, 0x37, 0x14, 0x0E, 0x89, 0xD0, 0x10, 0xD6,
             0x50, 0x1F, 0x22, 0x61, 0x97, 0x18, 0x04, 0xDE,
             0x73, 0x68, 0x0F, 0xE6, 0x1C, 0x23, 0x5C, 0x8F,
             0x4E, 0x63, 0x1F, 0xF0, 0x6D, 0xBD, 0xEE, 0x66,
             0x6D, 0xBB, 0x9A, 0xFB, 0xFD, 0xA3, 0xB9, 0x71,
             0xC3, 0x29, 0x0D, 0x7B, 0xDE, 0xF5, 0xC5, 0x78,
             0x5A, 0x07, 0x1B, 0xE9, 0x4A, 0xE1, 0x8A, 0x0B,
             0x2E, 0xD8, 0xAE, 0x67, 0x9A, 0xBA, 0xA6, 0x10,
             0x85, 0x28, 0xA8, 0x5E, 0x31, 0x7F, 0x87, 0xA8,
             0x99, 0xC5, 0x89, 0xF4, 0xA8, 0xAD, 0x42, 0x90,
             0xA6, 0xCA, 0x1E, 0xF9, 0xF1, 0x4D, 0x8D, 0x0A,
             0x7A, 0x66, 0xDC, 0x75, 0x0B, 0x69, 0xB1, 0x9C,
             0xB2, 0x58, 0x28, 0xC3, 0xEA, 0xF0, 0x42, 0x21,
             0x5C, 0x09, 0xAA, 0xD4, 0xA9, 0x54, 0xE8, 0x55 },
           /* p */
           2048,
           { 0xE0, 0x41, 0xBD, 0xF1, 0xC9, 0xB5, 0x69, 0xAC,
             0xF5, 0xE8, 0x02, 0x2D, 0x21, 0x1B, 0x87, 0x1B,
             0x5F, 0x29, 0x21, 0x41, 0xA5, 0x89, 0xFD, 0x0F,
             0x6D, 0xCB, 0x59, 0x47, 0x6B, 0x1C, 0x1D, 0xA4,
             0x01, 0x8D, 0xD7, 0xA1, 0xE1, 0x08, 0x39, 0x32,
             0x74, 0x5E, 0xF3, 0xC6, 0x6C, 0xF7, 0xFF, 0x31,
             0x3E, 0xED, 0x4C, 0xB1, 0x68, 0x1D, 0xEF, 0x9D,
             0x29, 0xCC, 0x3F, 0xE8, 0x7A, 0xF7, 0xAD, 0x19,
             0xE9, 0xEF, 0x34, 0x56, 0x62, 0xC9, 0xC4, 0xF4,
             0xE6, 0xE7, 0x07, 0xAA, 0x4E, 0x99, 0x49, 0x63,
             0x4C, 0x08, 0x64, 0x71, 0xA5, 0x5B, 0x67, 0x46,
             0xC2, 0xAE, 0xEF, 0x87, 0x71, 0xEF, 0x21, 0xA2,
             0xEE, 0x8A, 0xB4, 0xDE, 0xC4, 0xC2, 0x04, 0x3C,
             0x70, 0xCF, 0xBA, 0x89, 0xE5, 0xEB, 0x2F, 0x62,
             0xEA, 0x07, 0xC7, 0x4B, 0xD4, 0x16, 0x67, 0x69,
             0x12, 0xA9, 0x58, 0x9F, 0xB3, 0xED, 0x70, 0x28,
             0x8F, 0x8A, 0x03, 0xD1, 0x91, 0xC5, 0x8A, 0x88,
             0x96, 0xE8, 0xB2, 0x0F, 0x1E, 0xDE, 0x91, 0x80,
             0xCE, 0xD3, 0x03, 0x59, 0xF7, 0x5F, 0x48, 0xAF,
             0xE9, 0x7C, 0x46, 0xEE, 0x59, 0xC9, 0x27, 0x1E,
             0x71, 0x37, 0x55, 0x4A, 0xD7, 0x05, 0x56, 0x17,
             0x84, 0x8F, 0xD3, 0x04, 0x1C, 0xD6, 0x30, 0x47,
             0xF6, 0x46, 0x2C, 0x0E, 0x66, 0xE1, 0x83, 0x9F,
             0x63, 0xC6, 0x12, 0xD4, 0xA3, 0x57, 0xF5, 0xE5,
             0x76, 0x35, 0x6A, 0xAA, 0xE7, 0xC6, 0x4A, 0xC0,
             0xBF, 0xD9, 0xD6, 0x5E, 0xDF, 0x4B, 0x2F, 0x34,
             0xDA, 0xDB, 0xDF, 0x69, 0x06, 0x20, 0xC8, 0x95,
             0xCA, 0x44, 0xD9, 0x61, 0xDA, 0x05, 0xB1, 0x36,
             0x2B, 0x4A, 0xD5, 0xDA, 0xAC, 0xB9, 0x0F, 0xF5,
             0x86, 0x33, 0x5E, 0xCD, 0x7E, 0x1D, 0x7A, 0x16,
             0x00, 0xCB, 0x1A, 0xB3, 0x72, 0x69, 0x5B, 0x6E,
             0xC7, 0x71, 0x76, 0x21, 0xDB, 0xBE, 0x93, 0x57 },
           /* q */
           2048,
           { 0xCC, 0xF5, 0x51, 0x29, 0xD3, 0xB9, 0x24, 0xC8,
             0x38, 0xA7, 0x6C, 0xD3, 0x69, 0xD4, 0x6E, 0x9C,
             0xB8, 0x13, 0xFE, 0x3B, 0x39, 0xBA, 0xF1, 0xEB,
             0x10, 0x18, 0x47, 0xD3, 0x1D, 0x09, 0x13, 0x50,
             0x03, 0xAB, 0x2F, 0xC2, 0x39, 0x43, 0x1C, 0xDA,
             0x6E, 0x99, 0x08, 0x88, 0x3D, 0xE8, 0xA0, 0x54,
             0x6E, 0x35, 0x28, 0x37, 0xD4, 0xEB, 0x95, 0xCB,
             0x41, 0xD8, 0xEE, 0xC1, 0x4A, 0x66, 0xCD, 0x38,
             0xC2, 0x24, 0x7E, 0x82, 0xA3, 0x94, 0x39, 0x29,
             0x27, 0xBB, 0xF5, 0x70, 0xA8, 0x65, 0x5E, 0x0F,
             0x2A, 0xC2, 0x43, 0xE5, 0xFB, 0x87, 0x6F, 0xD2,
             0x0B, 0x48, 0x76, 0x73, 0xA2, 0x77, 0x2D, 0xA9,
             0x70, 0xC1, 0xDF, 0x47, 0xA3, 0x2D, 0xEA, 0x8A,
             0x75, 0xE7, 0x09, 0x54, 0x73, 0x22, 0x9C, 0x69,
             0x3C, 0x88, 0x6A, 0x31, 0x6D, 0x2C, 0xEC, 0xBF,
             0x03, 0x59, 0x7B, 0x04, 0xCA, 0x9E, 0xCA, 0xBD,
             0xA3, 0x36, 0x6E, 0x07, 0x64, 0x88, 0x05, 0x9B,
             0x24, 0x59, 0x6F, 0x5D, 0xF6, 0xE8, 0x56, 0x97,
             0xDB, 0xE6, 0x2A, 0xB2, 0xF8, 0xCC, 0x71, 0xAC,
             0x7F, 0x74, 0x3B, 0x64, 0x12, 0x6D, 0x01, 0xF2,
             0xB3, 0x61, 0x27, 0x16, 0xEC, 0xA7, 0x69, 0x75,
             0xE5, 0x14, 0xED, 0x4D, 0x78, 0xA3, 0x22, 0x90,
             0xBE, 0x0A, 0x82, 0xF1, 0x44, 0x14, 0x99, 0x2B,
             0xD1, 0x80, 0x3D, 0xAD, 0xC9, 0x83, 0xDD, 0xF2,
             0x76, 0xD2, 0xCA, 0xE1, 0xA0, 0xA9, 0x03, 0xF9,
             0x1E, 0x78, 0xBE, 0x3C, 0x0B, 0xCA, 0xF5, 0x8F,
             0x3C, 0xE9, 0x8D, 0x12, 0x3A, 0xA6, 0xC8, 0x5F,
             0x65, 0x51, 0xC5, 0x70, 0x07, 0xFE, 0x47, 0x7A,
             0xC8, 0x7E, 0x03, 0x8B, 0x9A, 0x94, 0xAC, 0xC6,
             0x20, 0xDE, 0x12, 0x25, 0x81, 0x05, 0x34, 0x4A,
             0x0C, 0xFB, 0x37, 0x65, 0x50, 0x5E, 0x8E, 0x7E,
             0xC8, 0x6A, 0xC0, 0x86, 0xF6, 0x55, 0x64, 0x23 },
           /* u */
           2048,
           { 0xD1, 0x0C, 0x91, 0x8D, 0xA9, 0xF2, 0x6D, 0xA9,
             0x4D, 0xFF, 0x3B, 0x09, 0x24, 0x3C, 0x8C, 0xC3,
             0xD4, 0x39, 0x02, 0x6D, 0xE6, 0x2B, 0x9E, 0x9F,
             0x37, 0xAC, 0x60, 0xBB, 0xD7, 0xA9, 0x52, 0xCB,
             0x07, 0x84, 0x94, 0xBD, 0x73, 0x7E, 0xCC, 0x3A,
             0x65, 0x0C, 0x93, 0xC4, 0x2E, 0xD7, 0xF6, 0x49,
             0x02, 0x07, 0xAE, 0x99, 0x6B, 0x3C, 0xD1, 0xFF,
             0x1F, 0x4D, 0x63, 0x9D, 0x61, 0xDD, 0xD1, 0xE7,
             0x12, 0x8D, 0x56, 0x3C, 0x1C, 0x16, 0xC8, 0xB3,
             0x9D, 0x94, 0xD5, 0xDE, 0x5E, 0x93, 0x7F, 0xE6,
             0x5A, 0x38, 0xB8, 0x19, 0xE4, 0x69, 0xF8, 0x8C,
             0x3C, 0xE0, 0x25, 0x21, 0xE2, 0xAD, 0xA9, 0xE3,
             0x46, 0xE6, 0xA1, 0xBD, 0x51, 0x27, 0xC7, 0xBD,
             0xB2, 0x1D, 0xA2, 0xC6, 0x11, 0xE3, 0x5F, 0x6C,
             0x89, 0xE7, 0xDD, 0x66, 0xA0, 0x66, 0xCB, 0x23,
             0x3E, 0xF9, 0x6B, 0xAD, 0x1A, 0xD3, 0x99, 0x94,
             0x0C, 0xAD, 0x05, 0x5A, 0xDF, 0x5C, 0x58, 0x79,
             0xF8, 0x30, 0xA8, 0x08, 0x3C, 0xA6, 0xD6, 0xC0,
             0x58, 0x58, 0xC2, 0x66, 0x03, 0x0A, 0x33, 0xBF,
             0xB4, 0xAD, 0x83, 0xB5, 0xCC, 0x92, 0x9F, 0x2F,
             0x6C, 0xA2, 0x1E, 0x50, 0x29, 0x54, 0x2B, 0x8A,
             0xEB, 0xE7, 0x6B, 0x69, 0x44, 0xE1, 0x86, 0x3E,
             0x39, 0x47, 0x3B, 0x6E, 0xD9, 0xAD, 0x92, 0x6A,
             0x7D, 0xBF, 0xE2, 0xC7, 0x28, 0xE2, 0x3C, 0x74,
             0xF6, 0x9B, 0xB0, 0xE0, 0x54, 0xF1, 0x9F, 0x14,
             0x6C, 0xE1, 0x9E, 0x1D, 0x23, 0x6B, 0x65, 0x34,
             0x30, 0xA7, 0x1D, 0xC4, 0xA7, 0x4A, 0xE2, 0x0E,
             0x0D, 0x14, 0x13, 0x31, 0x66, 0xA1, 0x8A, 0xDF,
             0x6E, 0xF7, 0xFE, 0xD9, 0x5C, 0xC4, 0x64, 0x35,
             0xFF, 0x4C, 0x96, 0x23, 0x2B, 0xD5, 0x64, 0x03,
             0xCC, 0x39, 0xFB, 0x16, 0xAD, 0xF2, 0x24, 0xB4,
             0xFD, 0xEB, 0x8A, 0xBA, 0xF4, 0x91, 0x31, 0xBF },
           /* exponent1 */
           2046,
           { 0x2F, 0x7C, 0x1C, 0x31, 0x37, 0x69, 0xCF, 0x6F,
             0x8D, 0x3E, 0x4C, 0x3F, 0xAC, 0x13, 0xFD, 0x1E,
             0xC1, 0x9E, 0x9E, 0xE9, 0x1C, 0x99, 0x44, 0x59,
             0x61, 0x01, 0x3E, 0xED, 0x4D, 0x73, 0xCD, 0x9E,
             0xED, 0xA9, 0x50, 0x30, 0x79, 0xCA, 0xD8, 0xF9,
             0xA3, 0x04, 0x7C, 0x0F, 0xD7, 0x01, 0x08, 0x2B,
             0x30, 0x4C, 0xE5, 0x01, 0x67, 0xAF, 0x77, 0x0E,
             0x4B, 0x4C, 0x71, 0x77, 0xD3, 0x99, 0xE0, 0x30,
             0x6D, 0x85, 0x76, 0x0A, 0x98, 0xAE, 0x6A, 0xA3,
             0x04, 0xC5, 0x84, 0xAC, 0xFE, 0x29, 0x9D, 0x0D,
             0x86, 0x8A, 0xFC, 0x61, 0xC8, 0x06, 0xBB, 0xAE,
             0x93, 0x08, 0xA1, 0xB5, 0x87, 0x5D, 0x80, 0x3C,
             0xD4, 0xCF, 0xD0, 0x0E, 0x9F, 0x91, 0x09, 0x7E,
             0x96, 0xD0, 0x95, 0x8A, 0x1F, 0x82, 0x16, 0x2D,
             0x96, 0xAA, 0x80, 0xFB, 0xC0, 0x73, 0xE1, 0xFF,
             0xB0, 0xB0, 0xE5, 0x10, 0x23, 0xF4, 0x31, 0xDC,
             0x94, 0xD0, 0x3F, 0x90, 0xBF, 0x92, 0x19, 0x8C,
             0x64, 0x8F, 0xEF, 0x2C, 0x1E, 0x78, 0x38, 0x4D,
             0x12, 0xFE, 0x41, 0x66, 0x6A, 0x67, 0xE5, 0xA7,
             0x42, 0x04, 0x4B, 0xAC, 0xAA, 0x9C, 0x5A, 0x49,
             0x2A, 0xE5, 0xF1, 0x8C, 0x80, 0x4D, 0x23, 0xF6,
             0xA4, 0xDE, 0x23, 0x6B, 0x6A, 0x83, 0xBC, 0x03,
             0x70, 0xD5, 0x58, 0xFC, 0xCF, 0xB2, 0x0E, 0xC1,
             0xD0, 0x49, 0x9F, 0xB1, 0x20, 0xC9, 0x3E, 0x4B,
             0x11, 0x25, 0xAC, 0x69, 0x75, 0xDC, 0x59, 0xF5,
             0xC8, 0x69, 0xE2, 0xE7, 0x81, 0xD6, 0x94, 0xAF,
             0x57, 0x6C, 0x59, 0x39, 0x0E, 0xD0, 0x20, 0x48,
             0xFF, 0x64, 0x66, 0xB7, 0x3E, 0x88, 0x18, 0x07,
             0x05, 0x51, 0xBA, 0x48, 0xAC, 0x6C, 0x1F, 0x41,
             0xF8, 0xE1, 0xA5, 0xC0, 0x53, 0x65, 0x00, 0x75,
             0xEA, 0x43, 0x17, 0x6B, 0x49, 0xDD, 0x9F, 0x3B,
             0xAC, 0xC5, 0x8C, 0xA3, 0x0C, 0xB9, 0xA4, 0xCF },
           /* exponent2 */
           2047,
           { 0x57, 0x5A, 0x87, 0x09, 0x28, 0xAF, 0xD4, 0x39,
             0x71, 0xCC, 0x09, 0xD9, 0xE1, 0x55, 0x24, 0xFF,
             0xAE, 0x84, 0xF6, 0xEA, 0x0F, 0x24, 0xDA, 0x4E,
             0xB1, 0x41, 0x67, 0xFB, 0x56, 0x78, 0xB3, 0xBE,
             0x7A, 0x91, 0xCF, 0x7D, 0x1C, 0x22, 0xBA, 0x7D,
             0x6E, 0x7D, 0xD2, 0xE1, 0x1E, 0x61, 0xB3, 0x53,
             0xC8, 0xD4, 0xE7, 0x1B, 0x44, 0xA8, 0x53, 0xE3,
             0x99, 0x60, 0xF8, 0x01, 0x71, 0xD0, 0x76, 0xCF,
             0x26, 0x0F, 0x9F, 0xCB, 0xD6, 0x24, 0x2A, 0x68,
             0x9C, 0x02, 0xC4, 0x0D, 0x0B, 0xF8, 0x88, 0x2A,
             0x36, 0xB3, 0x2D, 0x75, 0x2B, 0xCB, 0x01, 0xA1,
             0xA8, 0x25, 0x6E, 0x36, 0xC2, 0x9B, 0xC0, 0xDE,
             0x62, 0xAC, 0x7E, 0x99, 0x6D, 0xB6, 0xF8, 0x2B,
             0xA3, 0x2C, 0xA1, 0x11, 0x59, 0x30, 0xFB, 0x30,
             0xEF, 0x17, 0xC5, 0x0A, 0xE3, 0xD9, 0x2D, 0xDE,
             0x0B, 0x73, 0x6B, 0xB7, 0x13, 0x14, 0xB2, 0x9C,
             0x38, 0x9F, 0xCE, 0x2D, 0x60, 0x6F, 0x88, 0xD4,
             0x22, 0x9D, 0xEB, 0x95, 0x44, 0xD2, 0xA9, 0x75,
             0x77, 0xC7, 0x95, 0x93, 0x49, 0xEE, 0xF8, 0xD3,
             0xE8, 0x4E, 0x85, 0xB1, 0x95, 0x18, 0xD8, 0xA7,
             0xB4, 0x44, 0x48, 0x00, 0xC1, 0x44, 0x68, 0xF2,
             0x52, 0x7C, 0xA4, 0xD7, 0x4B, 0xFF, 0x5B, 0x90,
             0x0D, 0x2F, 0x35, 0xB7, 0xD6, 0xA8, 0x60, 0xD0,
             0x08, 0x2E, 0x7C, 0x1B, 0x41, 0xB3, 0xEE, 0x38,
             0x94, 0xE4, 0x2A, 0x8C, 0x17, 0x89, 0x71, 0xA4,
             0x0F, 0x94, 0xAE, 0x9F, 0xB0, 0xF7, 0x03, 0xC9,
             0xD4, 0xD0, 0x45, 0xCB, 0xEB, 0x2B, 0x82, 0x63,
             0x06, 0x2F, 0xDF, 0xD2, 0x6B, 0xD5, 0xB8, 0x69,
             0x60, 0x62, 0x34, 0xE8, 0x9F, 0x2D, 0x96, 0xA5,
             0xAB, 0x04, 0x7A, 0xFF, 0x79, 0x09, 0xDA, 0xCB,
             0x64, 0xD4, 0xFD, 0x3B, 0x35, 0x11, 0xD7, 0xF1,
             0xB9, 0x41, 0xA6, 0x64, 0xDF, 0x40, 0x6D, 0xB9 }

   RSA-4096 key in encoded form:

   -----BEGIN RSA PRIVATE KEY-----
   MIIJKAIBAAKCAgEAs4tJYOY75qjbqJqCl47x9jJE5Vd9jPWGFtXKV1nUnMjZNsM4
   qjy5sRHBSX5bUa9pLyYR5on3Z1SAwLD0w2VPQ6+F/oyK1zTgQqitoF/XZQjgC6D3
   VsNEO76DPqfRANT7Nn7r1gvbZIZ3/H3rlCRNrRr47tHGWBLAPnxz9/NY6UG8ZkWP
   97uXpJqYoRgH4CwaO5rTOlc64YDh/0Mq5VgMycq/q2AvMlvNoJfoe8em1040qH1g
   ikP+suT/8fS452hqmEddtRpuvQgXKldBd0kkiyFVyLkG4NVA6Mso9MAK3J/kdYoa
   w2SrOeThVSiYVEQVP+7GrUxTSLLjj/VQ9fpYM5eTNzDICIG/Ee7o/jhtW1EoSamD
   mUOr89lyIHaXuOwkEaJhnVXKBCM8WiztxvKG2CnQ6Dcge3ZSmqJEhyEmjcAVC7ew
   fnMxOnE+WJW6rzrf+mA5WMVn+FzyWx2AondWow0aUKHkaY7amhIrsKp6YPfNImyx
   Flz8+cqDCmBswPsUh/JJ5eDHHIhibFcSgIHedsEjhLbUSLZ/DnEjru90qIWWA3R1
   VIPykKfeZkZeInsrFzGPikkFKwFF+6KDdyvCmltYEqzO46tigXAZ5UgH8oiXEre4
   8wO6X+FH+cLzQ0q3A8HZRnNDgqCjU/Tgy76iaku/Ic6eteedR1fX3gJ/IOUCAwEA
   AQKCAgBq0bC7fN8gkU/2lM6jewFL14aT6CSjS6QWS+XRaHmNOhW5dhZteimERqr3
   nbyY8cKjsYOu5GCUUnszqVRGOC0beP9Afb9Q4H2YSyDZrIvK6afaY08kiJI89VDC
   Yzd+xjgbqRGIzI8f1LzoNMaG4b5xAf4eoCHgXm+P/Z1FZLt+M4TyV+qamjpTTUMH
   fPOalMKaubd4G1PFvFc49m47+tHI8N5uCJCr5mCFbjt8AUGrETVVFRrtyBxttL7t
   5gpoawAYT0VaLTq7LmgR4c3qOVMLj66o+CQ2ecnfdpeMXgFYV6ylnZ/kpi0VCa5i
   av+OCt+VpOsBScq3Eu8+w9YCMopsUCG6GzW4WD2akEBVA/X6D0JMcoYj/IHT3Xv/
   G/eMji69A6URLetliZhuSb0wBxrYQaPMqAdsz8eUYzCx/RwhKtPr032aTQqWlbgW
   igiJMn1SbxbRVjf6nb8EsLg92LXEBS3FOLbK6ckuyXAQei8e5NR6ZcyluVluQnSR
   m+fR7JDkUP5YWNwuAehOvZIH2Oog+jcUDonQENZQHyJhlxgE3nNoD+YcI1yPTmMf
   8G297mZtu5r7/aO5ccMpDXve9cV4Wgcb6Urhigsu2K5nmrqmEIUoqF4xf4eomcWJ
   9KitQpCmyh758U2NCnpm3HULabGcslgow+rwQiFcCarUqVToVQKCAQEA4EG98cm1
   aaz16AItIRuHG18pIUGlif0PbctZR2scHaQBjdeh4Qg5MnRe88Zs9/8xPu1MsWgd
   750pzD/oevetGenvNFZiycT05ucHqk6ZSWNMCGRxpVtnRsKu74dx7yGi7oq03sTC
   BDxwz7qJ5esvYuoHx0vUFmdpEqlYn7PtcCiPigPRkcWKiJbosg8e3pGAztMDWfdf
   SK/pfEbuWcknHnE3VUrXBVYXhI/TBBzWMEf2RiwOZuGDn2PGEtSjV/XldjVqqufG
   SsC/2dZe30svNNrb32kGIMiVykTZYdoFsTYrStXarLkP9YYzXs1+HXoWAMsas3Jp
   W27HcXYh276TVwKCAQEAzPVRKdO5JMg4p2zTadRunLgT/js5uvHrEBhH0x0JE1AD
   qy/COUMc2m6ZCIg96KBUbjUoN9TrlctB2O7BSmbNOMIkfoKjlDkpJ7v1cKhlXg8q
   wkPl+4dv0gtIdnOidy2pcMHfR6Mt6op15wlUcyKcaTyIajFtLOy/A1l7BMqeyr2j
   Nm4HZIgFmyRZb1326FaX2+YqsvjMcax/dDtkEm0B8rNhJxbsp2l15RTtTXijIpC+
   CoLxRBSZK9GAPa3Jg93ydtLK4aCpA/keeL48C8r1jzzpjRI6pshfZVHFcAf+R3rI
   fgOLmpSsxiDeEiWBBTRKDPs3ZVBejn7IasCG9lVkIwKCAQAvfBwxN2nPb40+TD+s
   E/0ewZ6e6RyZRFlhAT7tTXPNnu2pUDB5ytj5owR8D9cBCCswTOUBZ693DktMcXfT
   meAwbYV2CpiuaqMExYSs/imdDYaK/GHIBruukwihtYddgDzUz9AOn5EJfpbQlYof
   ghYtlqqA+8Bz4f+wsOUQI/Qx3JTQP5C/khmMZI/vLB54OE0S/kFmamflp0IES6yq
   nFpJKuXxjIBNI/ak3iNraoO8A3DVWPzPsg7B0EmfsSDJPksRJaxpddxZ9chp4ueB
   1pSvV2xZOQ7QIEj/ZGa3PogYBwVRukisbB9B+OGlwFNlAHXqQxdrSd2fO6zFjKMM
   uaTPAoIBAFdahwkor9Q5ccwJ2eFVJP+uhPbqDyTaTrFBZ/tWeLO+epHPfRwiun1u
   fdLhHmGzU8jU5xtEqFPjmWD4AXHQds8mD5/L1iQqaJwCxA0L+IgqNrMtdSvLAaGo
   JW42wpvA3mKsfplttvgroyyhEVkw+zDvF8UK49kt3gtza7cTFLKcOJ/OLWBviNQi
   neuVRNKpdXfHlZNJ7vjT6E6FsZUY2Ke0REgAwURo8lJ8pNdL/1uQDS81t9aoYNAI
   LnwbQbPuOJTkKowXiXGkD5Sun7D3A8nU0EXL6yuCYwYv39Jr1bhpYGI06J8tlqWr
   BHr/eQnay2TU/Ts1EdfxuUGmZN9AbbkCggEBANEMkY2p8m2pTf87CSQ8jMPUOQJt
   5iuenzesYLvXqVLLB4SUvXN+zDplDJPELtf2SQIHrplrPNH/H01jnWHd0ecSjVY8
   HBbIs52U1d5ek3/mWji4GeRp+Iw84CUh4q2p40bmob1RJ8e9sh2ixhHjX2yJ591m
   oGbLIz75a60a05mUDK0FWt9cWHn4MKgIPKbWwFhYwmYDCjO/tK2DtcySny9soh5Q
   KVQriuvna2lE4YY+OUc7btmtkmp9v+LHKOI8dPabsOBU8Z8UbOGeHSNrZTQwpx3E
   p0riDg0UEzFmoYrfbvf+2VzEZDX/TJYjK9VkA8w5+xat8iS0/euKuvSRMb8=
   -----END RSA PRIVATE KEY-----

2.2.  DLP Keys

   The following publicly known test keys may be used for DLP-based
   algorithms such as DSA, DH, and Elgamal.

   DLP-1024 key "testDLP1024":

           /* p */
           1018,
           { 0x03, 0x0C, 0xDF, 0xC3, 0x8F, 0xC3, 0xE4, 0x21,
             0x27, 0x90, 0xB0, 0xA4, 0x1E, 0x45, 0xB4, 0xE4,
             0xE8, 0x80, 0xDE, 0x8A, 0xBF, 0xD3, 0xAE, 0xCA,
             0x0B, 0x23, 0x8F, 0xB6, 0xCD, 0x73, 0x0C, 0xC3,
             0x18, 0x76, 0x93, 0x36, 0xD5, 0xB1, 0x80, 0xB2,
             0x80, 0x2A, 0x01, 0xBE, 0x4B, 0xC1, 0xAB, 0x84,
             0xFC, 0xE2, 0xFF, 0x48, 0x9B, 0x50, 0xC2, 0xD2,
             0x9D, 0xE9, 0x1E, 0xC0, 0xE6, 0x5B, 0x60, 0x64,
             0xFD, 0x0D, 0xE5, 0x37, 0xEA, 0xBA, 0x1C, 0x6C,
             0xDD, 0x27, 0xDC, 0x30, 0x30, 0x48, 0x1E, 0x8B,
             0xB9, 0x60, 0xAA, 0x8B, 0x8A, 0xEF, 0x93, 0x35,
             0x30, 0xE6, 0xB1, 0xCC, 0x51, 0x60, 0xBB, 0xFA,
             0xAF, 0x85, 0x0F, 0xF6, 0x57, 0x81, 0x12, 0x33,
             0x7D, 0x53, 0x03, 0x4E, 0x41, 0x63, 0xDC, 0x65,
             0x03, 0xBD, 0xF8, 0x89, 0x25, 0x81, 0x14, 0x1F,
             0xAB, 0x82, 0x55, 0xB6, 0xD9, 0x72, 0x7B, 0xB3 },
           /* q */
           160,
           { 0xEC, 0x41, 0xB9, 0xC0, 0x62, 0x1D, 0x5B, 0xDC,
             0xAF, 0x11, 0xD5, 0x19, 0x8F, 0x72, 0x08, 0x88,
             0x2E, 0x65, 0xBB, 0xDF },
           /* g */
           1017,
           { 0x01, 0x64, 0x87, 0xAC, 0xCF, 0xCD, 0x95, 0x50,
             0x51, 0xE0, 0x6E, 0x1C, 0x5B, 0xEF, 0x45, 0x2C,
             0x12, 0x63, 0xC7, 0x5D, 0x2B, 0x36, 0x50, 0x4F,
             0xB4, 0x27, 0x57, 0x35, 0xC2, 0x83, 0x32, 0x0B,
             0x63, 0xAC, 0x91, 0xC6, 0xF4, 0x02, 0x09, 0x32,
             0x53, 0x1C, 0xAB, 0x04, 0xB1, 0xCD, 0x72, 0xFD,
             0xF2, 0x9D, 0xE2, 0x4E, 0x27, 0x17, 0x97, 0xA7,
             0xDD, 0x21, 0x97, 0x67, 0x69, 0x31, 0xF9, 0x33,
             0x1D, 0x1F, 0x59, 0xEE, 0xE5, 0xBA, 0x2C, 0x7D,
             0x54, 0xAE, 0x13, 0x5C, 0x7F, 0x79, 0x41, 0x37,
             0xD8, 0xD8, 0x0E, 0xB6, 0x29, 0x28, 0x8E, 0x26,
             0x8A, 0x3B, 0xEB, 0xD2, 0x1F, 0x16, 0xA4, 0x03,
             0xF1, 0xD5, 0xDA, 0xD8, 0x3C, 0x1C, 0x47, 0x80,
             0x17, 0xA3, 0xCD, 0x26, 0x6F, 0x1B, 0xA4, 0x9B,
             0x89, 0x0D, 0xC0, 0x89, 0x21, 0x2E, 0x72, 0x26,
             0x1D, 0xA3, 0x67, 0xAF, 0x80, 0x3B, 0x02, 0x50 },
           /* x */
           157,
           { 0x11, 0xED, 0x99, 0x78, 0x5A, 0x81, 0x3A, 0x1B,
             0x0E, 0x96, 0xEC, 0xD3, 0x8D, 0x7F, 0x9B, 0xCE,
             0x9E, 0xBF, 0xD6, 0xFA },
           /* y */
           1018,
           { 0x02, 0x20, 0xB9, 0x42, 0xC2, 0x5C, 0x44, 0xDA,
             0x52, 0xB0, 0xD1, 0x76, 0x82, 0xEA, 0xC4, 0x36,
             0xEA, 0x7E, 0x81, 0xEC, 0x9F, 0x76, 0xE1, 0x05,
             0x75, 0x32, 0xAA, 0x67, 0xEA, 0xDD, 0x04, 0xAD,
             0xB8, 0xFD, 0x61, 0x81, 0xBA, 0x0B, 0x25, 0xF2,
             0x84, 0xDA, 0xAA, 0xAA, 0x05, 0xF3, 0xC8, 0x40,
             0x34, 0xD4, 0x17, 0xD3, 0x7B, 0x6E, 0x0A, 0x63,
             0x31, 0x8A, 0x0A, 0x79, 0x1F, 0x1D, 0x0D, 0xD4,
             0xF6, 0x8A, 0xFA, 0xE3, 0x35, 0xAA, 0x5D, 0xBE,
             0xA3, 0xF2, 0xF6, 0xD6, 0xDD, 0x73, 0x09, 0x26,
             0x24, 0x7F, 0xDC, 0x4D, 0x1B, 0x82, 0xDF, 0x8C,
             0x2D, 0x87, 0xAE, 0x8D, 0x36, 0xAD, 0xB9, 0xDD,
             0x25, 0x13, 0x57, 0x8E, 0x8B, 0x99, 0xAA, 0x6A,
             0x0E, 0xDF, 0x67, 0x5F, 0xFC, 0x2F, 0xDE, 0xB6,
             0x4B, 0x26, 0xE5, 0xBE, 0xD8, 0x53, 0x2D, 0xFD,
             0x98, 0x11, 0x0F, 0xCF, 0xC9, 0xED, 0xF9, 0x38 }

   DLP-1024 key in encoded form:

   -----BEGIN DSA PRIVATE KEY-----
   MIIBuQIBAAKBgAMM38OPw+QhJ5CwpB5FtOTogN6Kv9Ouygsjj7bNcwzDGHaTNtWx
   gLKAKgG+S8GrhPzi/0ibUMLSnekewOZbYGT9DeU36rocbN0n3DAwSB6LuWCqi4rv
   kzUw5rHMUWC7+q+FD/ZXgRIzfVMDTkFj3GUDvfiJJYEUH6uCVbbZcnuzAhUA7EG5
   wGIdW9yvEdUZj3IIiC5lu98CgYABZIesz82VUFHgbhxb70UsEmPHXSs2UE+0J1c1
   woMyC2Oskcb0AgkyUxyrBLHNcv3yneJOJxeXp90hl2dpMfkzHR9Z7uW6LH1UrhNc
   f3lBN9jYDrYpKI4mijvr0h8WpAPx1drYPBxHgBejzSZvG6SbiQ3AiSEuciYdo2ev
   gDsCUAKBgAIguULCXETaUrDRdoLqxDbqfoHsn3bhBXUyqmfq3QStuP1hgboLJfKE
   2qqqBfPIQDTUF9N7bgpjMYoKeR8dDdT2ivrjNapdvqPy9tbdcwkmJH/cTRuC34wt
   h66NNq253SUTV46LmapqDt9nX/wv3rZLJuW+2FMt/ZgRD8/J7fk4AhQR7Zl4WoE6
   Gw6W7NONf5vOnr/W+g==
   -----END DSA PRIVATE KEY-----

   DLP-2048 key "testDLP2048":

           /* p */
           2042,
           { 0x03, 0x2D, 0xD5, 0x53, 0x7D, 0x33, 0x7A, 0x91,
             0x34, 0x37, 0xD3, 0x5E, 0xA3, 0x43, 0x3D, 0xB0,
             0xE7, 0xB7, 0x21, 0x29, 0x8F, 0xBA, 0x87, 0x27,
             0xF2, 0xF9, 0xBE, 0x85, 0x6D, 0x6A, 0x14, 0x6B,
             0x92, 0x98, 0x8D, 0x50, 0x82, 0xF2, 0xC5, 0x72,
             0xB7, 0x70, 0x37, 0x63, 0xE8, 0x24, 0x54, 0xA7,
             0xA4, 0xA2, 0x25, 0x9B, 0x29, 0xAC, 0xE9, 0xB0,
             0xBC, 0x9B, 0x4B, 0x4D, 0x98, 0x5D, 0x6A, 0x9C,
             0x8C, 0xB6, 0x30, 0xE4, 0xE0, 0x9F, 0x48, 0x07,
             0x9F, 0x1B, 0xE8, 0x07, 0x69, 0x71, 0xDE, 0x92,
             0x68, 0x56, 0x70, 0xB9, 0x4C, 0xC9, 0x68, 0x7D,
             0xDC, 0x23, 0x3B, 0x30, 0xAF, 0x22, 0x94, 0xB0,
             0x30, 0xA6, 0xB4, 0x97, 0xF6, 0x46, 0xF9, 0x4E,
             0x1C, 0x17, 0xE8, 0x3A, 0x90, 0x4C, 0x2C, 0x1B,
             0x68, 0x44, 0x10, 0xCE, 0x04, 0x8F, 0xD9, 0xCD,
             0x64, 0x05, 0xA1, 0x4A, 0xA6, 0x8C, 0x2B, 0x8F,
             0x7F, 0x8B, 0xD0, 0x6E, 0x9F, 0x64, 0xC4, 0xBB,
             0x69, 0xCC, 0xBF, 0xBC, 0x80, 0x56, 0xAE, 0x41,
             0x4A, 0x8B, 0x2E, 0x35, 0xD6, 0x20, 0x5C, 0xDE,
             0xFB, 0x2A, 0x24, 0xA3, 0x79, 0xB8, 0xA1, 0x16,
             0x17, 0x50, 0x95, 0xFF, 0x57, 0xFF, 0x61, 0x55,
             0x12, 0x86, 0x86, 0xD9, 0x9B, 0x8E, 0x1F, 0x24,
             0x44, 0x63, 0x12, 0x71, 0xF0, 0x9C, 0x33, 0x4F,
             0x37, 0x22, 0x45, 0x2F, 0xE9, 0x26, 0x3F, 0xC3,
             0x34, 0x9E, 0x6F, 0x33, 0x07, 0xA6, 0x75, 0x4F,
             0xFD, 0x89, 0xD4, 0x43, 0x27, 0x38, 0x7D, 0xFD,
             0x40, 0x18, 0xA0, 0x2A, 0xEA, 0x6E, 0xF4, 0xC6,
             0x36, 0xA7, 0x69, 0xE7, 0xCE, 0xB7, 0x37, 0x19,
             0x19, 0x72, 0x49, 0xA8, 0x41, 0xA3, 0x0B, 0xE0,
             0xC4, 0xBE, 0x8E, 0xCB, 0x10, 0x7F, 0x38, 0x02,
             0xDC, 0x45, 0x83, 0xF8, 0xE0, 0x12, 0x94, 0xD5,
             0x2B, 0x62, 0x13, 0x67, 0xBD, 0x0C, 0x19, 0x53 },
           /* q */
           225,
           { 0x01, 0x95, 0x09, 0xB2, 0xED, 0xA8, 0x3B, 0x08,
             0x82, 0x73, 0x1B, 0x3F, 0xE8, 0x9C, 0x2E, 0xF6,
             0x9D, 0xB8, 0xD8, 0x36, 0x12, 0x34, 0x5D, 0x1A,
             0x66, 0xA5, 0x83, 0xB9, 0x11 },
           /* g */
           2040,
           { 0xAC, 0x5D, 0x12, 0x0E, 0x46, 0xD2, 0xBA, 0xD6,
             0x87, 0x88, 0x47, 0xCC, 0xE8, 0x70, 0xA6, 0x9E,
             0xDC, 0xAD, 0xC8, 0x6C, 0x85, 0x9C, 0x49, 0xBA,
             0xF7, 0xAD, 0xE4, 0x1E, 0xD9, 0x36, 0x8E, 0xC2,
             0x3B, 0x64, 0x54, 0xFB, 0x60, 0xEA, 0xDA, 0xAC,
             0xC6, 0x64, 0x2A, 0x6F, 0xDD, 0x32, 0x2B, 0x99,
             0xAB, 0x14, 0x75, 0x81, 0xB2, 0x1B, 0xEB, 0xE0,
             0x62, 0x94, 0xE3, 0x82, 0x0B, 0xC5, 0x56, 0xFA,
             0x54, 0x11, 0xB3, 0x1C, 0x37, 0x3B, 0x39, 0xA6,
             0x7D, 0x51, 0x8A, 0x54, 0x77, 0x13, 0x41, 0x5C,
             0x67, 0xAC, 0xEF, 0x18, 0xBC, 0x6B, 0xA9, 0x4C,
             0x95, 0x60, 0x0C, 0xB5, 0xBD, 0xA8, 0x3C, 0x84,
             0xAD, 0x58, 0xE5, 0x49, 0x1D, 0x26, 0x26, 0x1E,
             0xD4, 0xE5, 0x35, 0xAD, 0xB2, 0x2E, 0x35, 0xB0,
             0x6C, 0xC2, 0xB4, 0xC8, 0x9D, 0xA2, 0xDC, 0x63,
             0xE2, 0x9E, 0xDA, 0x06, 0xF0, 0x13, 0x80, 0x72,
             0x46, 0x55, 0x89, 0x32, 0xE9, 0xF2, 0xDC, 0x8B,
             0x93, 0x2E, 0x6B, 0x84, 0xB4, 0x07, 0xF5, 0x71,
             0x50, 0x9D, 0x06, 0xF7, 0x94, 0x30, 0xE9, 0x5D,
             0x46, 0xB2, 0xD0, 0x26, 0x14, 0x28, 0x84, 0x17,
             0x99, 0x98, 0x86, 0xA6, 0x71, 0x45, 0xED, 0x74,
             0x6A, 0x0C, 0xA8, 0xC0, 0x44, 0x41, 0x03, 0xF5,
             0x03, 0xE6, 0xBB, 0xE7, 0x45, 0x61, 0xC3, 0xAC,
             0xD1, 0x9A, 0xE5, 0x7A, 0x82, 0x67, 0xA1, 0xBC,
             0x3C, 0x49, 0x30, 0x83, 0xBB, 0x16, 0xC5, 0x97,
             0xA8, 0xAC, 0x99, 0x81, 0xFB, 0x70, 0x45, 0x87,
             0x17, 0xFB, 0x64, 0x9C, 0xA4, 0x61, 0xD4, 0x70,
             0xB4, 0xB3, 0x5E, 0x3E, 0x98, 0x64, 0xFA, 0x1A,
             0x59, 0x9B, 0xC0, 0x1E, 0x6F, 0xE9, 0x93, 0x0A,
             0x51, 0xF5, 0x79, 0xB0, 0x84, 0x01, 0x74, 0x25,
             0xB8, 0xD0, 0xA1, 0x02, 0x3F, 0xAE, 0xDD, 0xDC,
             0x57, 0xD1, 0xCE, 0x56, 0x25, 0x1C, 0xDA },
           /* x */
           223,
           { 0x64, 0x05, 0xBC, 0xDE, 0xB4, 0xF7, 0x68, 0x29,
             0x02, 0x23, 0xCE, 0x5D, 0xB5, 0x2A, 0x8A, 0x30,
             0xC2, 0x8A, 0xDC, 0x78, 0x02, 0xD9, 0x68, 0x1E,
             0xDC, 0xB4, 0x34, 0xE5 },
           /* y */
           2042,
           { 0x02, 0x30, 0x37, 0xB2, 0xD9, 0xC9, 0x9E, 0x75,
             0x3F, 0xD2, 0x79, 0xBF, 0xFC, 0xDE, 0xE9, 0x92,
             0x9C, 0x9B, 0xA1, 0xDE, 0xAA, 0x97, 0x0B, 0x03,
             0x72, 0xAF, 0x73, 0x35, 0xE5, 0x50, 0x21, 0x37,
             0x42, 0x99, 0xF3, 0x61, 0x02, 0x7C, 0x8D, 0x65,
             0xD5, 0x7A, 0xFB, 0x4D, 0x3C, 0xCD, 0x2B, 0x47,
             0x24, 0xB5, 0x3F, 0x09, 0xEB, 0xE2, 0x8C, 0xBF,
             0x49, 0x9F, 0x6B, 0x4F, 0x86, 0x33, 0x49, 0x19,
             0x8B, 0x24, 0xB2, 0xAB, 0x0D, 0x4C, 0xEC, 0xB6,
             0xC4, 0xFD, 0x7E, 0x67, 0x2D, 0x4B, 0x2A, 0xCA,
             0x9D, 0x39, 0xE3, 0xAE, 0x20, 0xF8, 0xEC, 0xD7,
             0xFD, 0x77, 0x10, 0x7C, 0xE5, 0x4A, 0x66, 0xDD,
             0xEE, 0x97, 0x44, 0xE4, 0x8C, 0xF8, 0xDD, 0x6B,
             0xA9, 0xA5, 0x28, 0xC7, 0x51, 0xF0, 0x08, 0xC6,
             0x6F, 0x19, 0x2A, 0x20, 0x4E, 0xC7, 0xF9, 0x38,
             0x76, 0x91, 0x01, 0x79, 0xB1, 0x31, 0x1D, 0x97,
             0x5B, 0x49, 0x25, 0xC5, 0x69, 0x90, 0x29, 0xFB,
             0xD1, 0x14, 0xA5, 0xE7, 0x90, 0x19, 0x0A, 0x4D,
             0x38, 0x9B, 0x94, 0x8F, 0x8F, 0x57, 0x6A, 0x8E,
             0x45, 0xA5, 0x6B, 0xE0, 0xD4, 0xFD, 0x6C, 0xEA,
             0x63, 0x1C, 0x5F, 0x53, 0x7E, 0xF9, 0x18, 0x59,
             0x8E, 0x30, 0x52, 0x2F, 0x93, 0x64, 0x50, 0x66,
             0x18, 0xC0, 0x45, 0x84, 0xCA, 0x6F, 0xD0, 0x75,
             0x12, 0x12, 0x21, 0xA4, 0x60, 0xF9, 0x80, 0xC5,
             0x4F, 0x80, 0x1D, 0x7D, 0x6D, 0x21, 0x9D, 0xF2,
             0xA1, 0xDB, 0xEA, 0x3C, 0x8A, 0x03, 0xA0, 0x9F,
             0x6B, 0xE9, 0x1B, 0xB6, 0x29, 0x6D, 0x79, 0x1A,
             0x2A, 0x83, 0x80, 0xE8, 0x9D, 0x0C, 0xDD, 0x26,
             0xF7, 0x66, 0x3E, 0x06, 0x9A, 0x83, 0x31, 0x49,
             0xAD, 0x44, 0x2B, 0x2C, 0x13, 0x98, 0x87, 0x71,
             0xF6, 0x54, 0xB8, 0x1F, 0x50, 0xE0, 0xD7, 0x26,
             0x42, 0x47, 0xD6, 0x78, 0xEA, 0xEB, 0xB0, 0xF9 }

   DLP-2048 key in encoded form:

   -----BEGIN DSA PRIVATE KEY-----
   MIIDTAIBAAKCAQADLdVTfTN6kTQ3016jQz2w57chKY+6hyfy+b6FbWoUa5KYjVCC
   8sVyt3A3Y+gkVKekoiWbKazpsLybS02YXWqcjLYw5OCfSAefG+gHaXHekmhWcLlM
   yWh93CM7MK8ilLAwprSX9kb5ThwX6DqQTCwbaEQQzgSP2c1kBaFKpowrj3+L0G6f
   ZMS7acy/vIBWrkFKiy411iBc3vsqJKN5uKEWF1CV/1f/YVUShobZm44fJERjEnHw
   nDNPNyJFL+kmP8M0nm8zB6Z1T/2J1EMnOH39QBigKupu9MY2p2nnzrc3GRlySahB
   owvgxL6OyxB/OALcRYP44BKU1StiE2e9DBlTAh0BlQmy7ag7CIJzGz/onC72nbjY
   NhI0XRpmpYO5EQKCAQAArF0SDkbSutaHiEfM6HCmntytyGyFnEm6963kHtk2jsI7
   ZFT7YOrarMZkKm/dMiuZqxR1gbIb6+BilOOCC8VW+lQRsxw3OzmmfVGKVHcTQVxn
   rO8YvGupTJVgDLW9qDyErVjlSR0mJh7U5TWtsi41sGzCtMidotxj4p7aBvATgHJG
   VYky6fLci5Mua4S0B/VxUJ0G95Qw6V1GstAmFCiEF5mYhqZxRe10agyowERBA/UD
   5rvnRWHDrNGa5XqCZ6G8PEkwg7sWxZeorJmB+3BFhxf7ZJykYdRwtLNePphk+hpZ
   m8Aeb+mTClH1ebCEAXQluNChAj+u3dxX0c5WJRzaAoIBAAIwN7LZyZ51P9J5v/ze
   6ZKcm6HeqpcLA3KvczXlUCE3QpnzYQJ8jWXVevtNPM0rRyS1Pwnr4oy/SZ9rT4Yz
   SRmLJLKrDUzstsT9fmctSyrKnTnjriD47Nf9dxB85Upm3e6XROSM+N1rqaUox1Hw
   CMZvGSogTsf5OHaRAXmxMR2XW0klxWmQKfvRFKXnkBkKTTiblI+PV2qORaVr4NT9
   bOpjHF9TfvkYWY4wUi+TZFBmGMBFhMpv0HUSEiGkYPmAxU+AHX1tIZ3yodvqPIoD
   oJ9r6Ru2KW15GiqDgOidDN0m92Y+BpqDMUmtRCssE5iHcfZUuB9Q4NcmQkfWeOrr
   sPkCHGQFvN6092gpAiPOXbUqijDCitx4AtloHty0NOU=
   -----END DSA PRIVATE KEY-----

   DLP-4096 key "testDLP4096":

           /* p */
           4086,
           { 0x31, 0xD2, 0x55, 0x5F, 0xB2, 0xE8, 0x89, 0xF3,
             0x20, 0x83, 0x78, 0x79, 0x5A, 0xF4, 0x88, 0x5B,
             0x62, 0xD0, 0x13, 0x58, 0xBD, 0xF1, 0x17, 0xC0,
             0xB8, 0xAD, 0x4D, 0x22, 0xBE, 0x62, 0xCC, 0x93,
             0x34, 0x5B, 0x6E, 0xA8, 0xFC, 0x54, 0x0B, 0x56,
             0x8F, 0x50, 0x95, 0xBB, 0xA0, 0x90, 0x3E, 0xC5,
             0xEE, 0xD8, 0xC6, 0xAE, 0x52, 0x5D, 0x9A, 0xA7,
             0xE4, 0x99, 0x79, 0xF0, 0x8E, 0x6C, 0x4E, 0xDB,
             0xF5, 0x6A, 0x93, 0x29, 0x09, 0xA0, 0x6B, 0x6D,
             0x1E, 0x07, 0x57, 0x95, 0x3F, 0x90, 0x5B, 0x55,
             0x52, 0x99, 0x31, 0x5F, 0x42, 0x48, 0xF5, 0x4B,
             0x81, 0xEF, 0x5F, 0x05, 0x4D, 0x8D, 0x82, 0x4E,
             0x12, 0xAE, 0xAB, 0x82, 0x4B, 0x2C, 0x2F, 0x4C,
             0x5E, 0xDE, 0x04, 0x60, 0x30, 0xDC, 0x3B, 0x16,
             0xC2, 0x80, 0x59, 0x56, 0x85, 0xCA, 0x38, 0xC6,
             0xE7, 0x13, 0xD8, 0x2E, 0x4D, 0x1B, 0xFC, 0xD3,
             0x3D, 0x87, 0xDE, 0x26, 0x95, 0x4B, 0xA0, 0x05,
             0xBC, 0x42, 0x17, 0x77, 0x39, 0xB2, 0x0F, 0x1E,
             0x46, 0x13, 0x80, 0x79, 0xED, 0xE5, 0x91, 0x64,
             0xCE, 0x67, 0x23, 0xE3, 0x51, 0xE4, 0xB2, 0xFC,
             0xD5, 0x0D, 0x6E, 0xAB, 0xB4, 0x5D, 0xA8, 0x8F,
             0xA4, 0xCD, 0x56, 0x24, 0x8A, 0xEA, 0x44, 0xAA,
             0x2E, 0x41, 0xB8, 0xFF, 0x28, 0xBD, 0x37, 0x88,
             0x00, 0x8C, 0x2E, 0xEF, 0x4B, 0xE1, 0x90, 0xA0,
             0xAB, 0x5D, 0x7D, 0x80, 0x3C, 0x9A, 0xBE, 0xD7,
             0xC7, 0xB7, 0x74, 0xB5, 0x0F, 0xA8, 0x38, 0x0D,
             0xD7, 0xFE, 0x2B, 0x3D, 0x84, 0x85, 0xA3, 0xD8,
             0x80, 0xEF, 0x51, 0xD5, 0x6B, 0x41, 0x1F, 0x73,
             0xE6, 0x59, 0xE7, 0x9E, 0x0B, 0xFF, 0x32, 0x14,
             0x53, 0x57, 0x3E, 0xC5, 0x0D, 0x9D, 0xD4, 0xD0,
             0xAE, 0xCA, 0x30, 0x9D, 0x39, 0xE4, 0x38, 0x86,
             0x27, 0x95, 0x03, 0xEF, 0x94, 0x98, 0x51, 0xE3,
             0xD4, 0xDC, 0x71, 0xAB, 0xF3, 0xA7, 0x88, 0x63,
             0xB9, 0x75, 0xC1, 0x06, 0x24, 0xCB, 0x51, 0x73,
             0x4C, 0xDB, 0x58, 0x2A, 0x3A, 0x48, 0xC6, 0xD7,
             0x08, 0x47, 0x83, 0x6E, 0x80, 0x8B, 0x0E, 0x22,
             0x48, 0xB8, 0xFA, 0x8A, 0x8C, 0x55, 0xA3, 0x57,
             0xE8, 0x30, 0x54, 0xD6, 0x48, 0xB2, 0xCC, 0xA5,
             0xB8, 0xA3, 0xB1, 0x68, 0x91, 0xAD, 0x52, 0x35,
             0x6E, 0x92, 0x87, 0x1A, 0xF5, 0x99, 0xA5, 0x6E,
             0x90, 0xC9, 0x34, 0x33, 0xA5, 0x4A, 0x52, 0xFD,
             0x42, 0xE2, 0xBE, 0x65, 0x15, 0xC8, 0xCE, 0xC3,
             0x73, 0x94, 0x07, 0x0C, 0x26, 0xCA, 0xC5, 0xCA,
             0x8C, 0x26, 0x1D, 0x2D, 0x50, 0x21, 0x88, 0x6B,
             0xB9, 0x4C, 0x4E, 0x99, 0xFA, 0x78, 0xD2, 0x53,
             0x7C, 0xCA, 0xF5, 0xA1, 0x92, 0xC9, 0xC2, 0xAF,
             0x77, 0xA0, 0x78, 0x33, 0x45, 0x1F, 0x12, 0x2D,
             0xA9, 0xE6, 0xFD, 0x7B, 0x83, 0x92, 0x12, 0x9E,
             0xE4, 0x9A, 0x56, 0x07, 0x5F, 0x1A, 0x37, 0x05,
             0x00, 0x4C, 0x06, 0xBD, 0x36, 0x7F, 0xBF, 0xCB,
             0x9A, 0x07, 0x4A, 0x02, 0xE1, 0x65, 0x25, 0x27,
             0x2D, 0xF9, 0xD3, 0x33, 0xCB, 0x91, 0x9B, 0x5B,
             0x61, 0x14, 0x07, 0xF7, 0xF7, 0xA4, 0xD9, 0xE1,
             0x1E, 0xD2, 0x85, 0xA4, 0x75, 0x95, 0xEA, 0x74,
             0x0C, 0xBF, 0xA1, 0x6B, 0xD2, 0xFB, 0xB8, 0x0A,
             0xD2, 0xA5, 0xE6, 0x36, 0x04, 0x47, 0x80, 0x8B,
             0x1E, 0xC5, 0x07, 0x58, 0xB8, 0x56, 0xF6, 0xDC,
             0xA4, 0x25, 0xD9, 0x36, 0xB4, 0x9E, 0xEA, 0x5B,
             0x7E, 0xAA, 0x40, 0x79, 0xA3, 0x15, 0x3D, 0xED,
             0x32, 0x12, 0x76, 0x4D, 0x00, 0x06, 0xF0, 0x09,
             0x36, 0x28, 0x4B, 0x96, 0xD6, 0x8B, 0xC9, 0x74,
             0xFD, 0xAF, 0x77, 0xB6, 0x45, 0x78, 0x36, 0x38,
             0xC5, 0x1E, 0xB1, 0x18, 0x8A, 0x91, 0x72, 0xA0,
             0x37, 0xDE, 0x49, 0xDA, 0x48, 0x1A, 0x9B },
           /* q */
           305,
           { 0x01, 0xFF, 0x30, 0x36, 0x06, 0x89, 0x3F, 0x53,
             0xBE, 0x41, 0x12, 0xF9, 0x60, 0x18, 0xF9, 0x9C,
             0xCF, 0xB9, 0x67, 0x82, 0x7E, 0x49, 0x40, 0x36,
             0x98, 0x2F, 0xAF, 0x24, 0x06, 0xD2, 0x5D, 0x8B,
             0xCC, 0x52, 0x48, 0xDB, 0x2B, 0xCB, 0x13 },
           /* g */
           4085,
           { 0x19, 0x89, 0x03, 0x1B, 0x12, 0xB8, 0x83, 0x5D,
             0x66, 0x5C, 0x9F, 0x42, 0x31, 0x05, 0x24, 0xA0,
             0x64, 0x9E, 0xEC, 0x4C, 0x2C, 0x4A, 0xBA, 0xAC,
             0xAD, 0x5D, 0x54, 0x8C, 0xE0, 0xFA, 0xF5, 0x3E,
             0xCA, 0x38, 0x67, 0xAA, 0xE6, 0x18, 0x7D, 0x5F,
             0x63, 0xC0, 0xF6, 0x6B, 0x56, 0xE8, 0x00, 0xAD,
             0x5D, 0x09, 0x58, 0x8C, 0xA4, 0x25, 0xBC, 0xE6,
             0xBD, 0x33, 0x97, 0x6B, 0xBA, 0xC9, 0x68, 0x63,
             0xD1, 0xC2, 0x6E, 0x4F, 0x48, 0x27, 0x67, 0x05,
             0x63, 0xFB, 0x9C, 0xA5, 0x16, 0x5C, 0x3C, 0x9F,
             0x14, 0x1D, 0x2E, 0x7D, 0x77, 0xA6, 0x11, 0x95,
             0x55, 0x4D, 0x9C, 0xE6, 0xA3, 0x25, 0xB9, 0x34,
             0x2A, 0x5F, 0x0A, 0xDE, 0x00, 0x7E, 0xED, 0x69,
             0xF3, 0x2C, 0x78, 0x67, 0x8C, 0x5F, 0x30, 0x2C,
             0xAF, 0x97, 0x62, 0xFC, 0xC0, 0xD6, 0x22, 0xD2,
             0xBF, 0xA5, 0xFF, 0x72, 0x4B, 0x59, 0x49, 0x21,
             0x1C, 0x66, 0x2E, 0xD3, 0xD8, 0x14, 0x1E, 0xAF,
             0xAB, 0xB6, 0x28, 0x65, 0xC2, 0xF2, 0xA6, 0x44,
             0xA5, 0xDC, 0x34, 0x0F, 0x24, 0x0F, 0x73, 0x61,
             0x53, 0x3C, 0x65, 0x64, 0xCD, 0x9E, 0x33, 0xB6,
             0x58, 0xC1, 0x39, 0x71, 0xEC, 0xDA, 0x66, 0x2E,
             0x1C, 0x79, 0xB5, 0x88, 0x7E, 0xA2, 0x46, 0x1E,
             0x35, 0xA6, 0xBA, 0x2B, 0xD0, 0x20, 0x80, 0xF8,
             0xE5, 0xC6, 0xC8, 0xBE, 0x7B, 0xFB, 0xB9, 0x6C,
             0xF4, 0x1F, 0x07, 0xD5, 0xBD, 0xC9, 0x65, 0x00,
             0xB5, 0x6C, 0x53, 0x4B, 0x70, 0x36, 0x99, 0x56,
             0x8F, 0x70, 0x0B, 0x9A, 0xD5, 0xEF, 0xFC, 0x1E,
             0xE8, 0xBE, 0x2F, 0x70, 0x39, 0x50, 0xAC, 0xD3,
             0xB8, 0x8C, 0x24, 0x3F, 0x82, 0xA2, 0xE9, 0xF5,
             0x01, 0xE3, 0x87, 0x84, 0x4E, 0x77, 0xAA, 0x90,
             0x2D, 0xC0, 0xD7, 0xD9, 0x6E, 0xBE, 0x4E, 0x4B,
             0xC8, 0xB3, 0xAB, 0x09, 0x64, 0xAC, 0x28, 0xB1,
             0x54, 0xCD, 0x15, 0x35, 0xA4, 0x06, 0x55, 0x40,
             0x83, 0x39, 0x8E, 0x0B, 0xE6, 0xAC, 0x9B, 0x26,
             0xFF, 0x9A, 0xF4, 0xC2, 0xCD, 0xA9, 0x55, 0x17,
             0x51, 0x15, 0x2F, 0xBD, 0x4C, 0xC2, 0xD7, 0xF1,
             0x9A, 0x9E, 0x7F, 0x41, 0xA5, 0x6E, 0xBB, 0xEF,
             0x3C, 0xD5, 0x1D, 0xF6, 0xB1, 0x08, 0x48, 0x06,
             0x15, 0xA8, 0xF3, 0xED, 0x99, 0x9F, 0xEC, 0x7F,
             0x0F, 0x3C, 0x53, 0x87, 0x55, 0x27, 0x70, 0x74,
             0xB3, 0xA8, 0x0D, 0x4B, 0x6A, 0x84, 0x71, 0x26,
             0xE1, 0xB9, 0xDF, 0xE2, 0x38, 0x96, 0xF5, 0xB1,
             0x97, 0x53, 0x83, 0x9B, 0x18, 0xA7, 0xE6, 0x69,
             0x3E, 0x9F, 0xB1, 0x3D, 0x11, 0x58, 0xA3, 0xAB,
             0xAF, 0x4E, 0x04, 0x62, 0x7D, 0xEB, 0x96, 0x12,
             0xD9, 0x59, 0x4D, 0x33, 0x26, 0x1A, 0xE5, 0x93,
             0x67, 0xFF, 0xCA, 0xDE, 0xC3, 0xB5, 0xAF, 0xFF,
             0xCB, 0xDF, 0xED, 0x45, 0x0B, 0x53, 0x8B, 0xC8,
             0xD8, 0x8D, 0x29, 0x8E, 0xDD, 0x27, 0xB3, 0x36,
             0xE8, 0xF5, 0xEE, 0x6D, 0x46, 0x1F, 0x57, 0x40,
             0x3B, 0xB4, 0x6D, 0xBC, 0x04, 0xB6, 0xD9, 0x00,
             0xC7, 0x48, 0x72, 0x8D, 0xE7, 0x8F, 0x68, 0x8F,
             0xCD, 0x9A, 0x90, 0x29, 0x4E, 0xEA, 0x95, 0xE7,
             0xCE, 0x48, 0x2A, 0x39, 0xB0, 0x62, 0xE8, 0x04,
             0xFC, 0xCB, 0x6E, 0xF7, 0xD1, 0x35, 0x94, 0xB9,
             0x35, 0x0E, 0xC2, 0x0F, 0xB5, 0x02, 0xA8, 0x4C,
             0x4E, 0x30, 0x96, 0xC5, 0x90, 0xAA, 0x29, 0x63,
             0x78, 0x79, 0x0D, 0x81, 0x9E, 0xC2, 0xC5, 0x0D,
             0xD5, 0xF5, 0x46, 0xF5, 0xE3, 0xE4, 0xD9, 0x69,
             0xEC, 0x33, 0xDA, 0x45, 0x52, 0x14, 0xD7, 0xA0,
             0x5C, 0xAA, 0xF8, 0x87, 0xB5, 0xE8, 0x9B, 0x09,
             0xE6, 0xB2, 0xCF, 0x0D, 0x56, 0x43, 0xC3, 0x85,
             0x48, 0x01, 0x8A, 0x87, 0x7B, 0x5A, 0x17, 0x72,
             0x40, 0x2B, 0x4B, 0x29, 0xF3, 0x5C, 0x8B },
           /* x */
           305,
           { 0x01, 0xA7, 0x77, 0x11, 0xB8, 0x9D, 0x45, 0x53,
             0x27, 0x29, 0x01, 0xBA, 0x09, 0x5A, 0x7F, 0xFC,
             0x14, 0x9C, 0x8C, 0x05, 0xB0, 0x2F, 0xDD, 0x04,
             0x0D, 0xC9, 0x98, 0x97, 0x11, 0x5B, 0xCE, 0xC3,
             0xE6, 0x14, 0xF2, 0x55, 0x7F, 0x9C, 0x0C },
           /* y */
           4086,
           { 0x2A, 0x49, 0x11, 0x73, 0x18, 0x65, 0x11, 0x4B,
             0x8A, 0x6C, 0x6F, 0x8E, 0x40, 0x7D, 0x55, 0xC3,
             0x9A, 0xB7, 0x10, 0xBB, 0x45, 0xCA, 0xBA, 0x94,
             0xE6, 0xB1, 0x85, 0x87, 0xD2, 0x8F, 0x9C, 0x6C,
             0x69, 0x4C, 0x01, 0x9A, 0x09, 0xB2, 0x6F, 0x44,
             0x8C, 0x2A, 0x33, 0x55, 0xA5, 0x67, 0xB1, 0xA0,
             0xC8, 0x61, 0x82, 0x2E, 0x19, 0xC6, 0xFA, 0xDE,
             0x8C, 0x43, 0xAA, 0x61, 0xC3, 0xBF, 0x39, 0xB6,
             0x95, 0xE2, 0xA2, 0x74, 0x55, 0x2F, 0xE8, 0x5C,
             0x76, 0x5B, 0x8A, 0x1E, 0xF7, 0x8D, 0x1B, 0x42,
             0x97, 0xEF, 0x4C, 0x31, 0x3F, 0xE8, 0xDB, 0xF2,
             0x22, 0x11, 0x30, 0xC5, 0xEE, 0x91, 0xF9, 0xE3,
             0xD3, 0xBB, 0xF2, 0x9C, 0xC4, 0x7B, 0x1B, 0xAB,
             0xAF, 0x17, 0x9C, 0xBA, 0x8B, 0xD4, 0x5B, 0xA9,
             0x61, 0xD7, 0x0A, 0xB6, 0xBD, 0x7A, 0xA0, 0x75,
             0xFB, 0x2A, 0x15, 0x33, 0x14, 0xFC, 0x3B, 0x2C,
             0x3B, 0x89, 0x86, 0x6E, 0x68, 0x2C, 0x7A, 0x95,
             0x8D, 0x3B, 0x78, 0x87, 0xF0, 0xD7, 0xD8, 0xF4,
             0x0D, 0xF5, 0x5E, 0x6E, 0x51, 0x5D, 0x1F, 0xBB,
             0x88, 0x77, 0x8E, 0xAF, 0x8E, 0xF1, 0xE8, 0xF3,
             0x11, 0x9A, 0x74, 0x98, 0x80, 0x66, 0x7C, 0xA8,
             0xEC, 0xC4, 0x6B, 0xFA, 0x10, 0xBA, 0xC4, 0x67,
             0x4B, 0x77, 0xB9, 0x4E, 0xB0, 0xE9, 0x2A, 0x76,
             0xA6, 0xC0, 0x81, 0x59, 0xD1, 0xF4, 0x06, 0xB6,
             0x68, 0x5F, 0xE8, 0x5B, 0x41, 0xA8, 0xD8, 0x04,
             0x93, 0x91, 0x8A, 0xF5, 0x29, 0x9A, 0x1C, 0x6A,
             0x11, 0x3D, 0xE2, 0xF9, 0x74, 0x27, 0xCD, 0x87,
             0xC4, 0xBA, 0x28, 0x2A, 0x65, 0x5D, 0x6A, 0x4E,
             0xE7, 0x15, 0x01, 0x2E, 0x0C, 0x75, 0x0C, 0xC3,
             0xB1, 0xE5, 0xC0, 0xF2, 0x2B, 0xC8, 0x2A, 0xD2,
             0x3E, 0xB4, 0xC0, 0xEC, 0xF4, 0x80, 0xAC, 0xB7,
             0xD7, 0x31, 0x21, 0x57, 0xDB, 0xB7, 0xE0, 0xE5,
             0x23, 0x78, 0xE9, 0xFF, 0x46, 0xEE, 0xEF, 0x04,
             0xAF, 0x47, 0x4F, 0x2C, 0x4C, 0x55, 0xDF, 0xFF,
             0xCF, 0x79, 0x8B, 0x90, 0x3F, 0x49, 0xEA, 0x43,
             0xD0, 0x60, 0xEF, 0x23, 0xED, 0x7D, 0x63, 0x89,
             0x7B, 0xCB, 0x2F, 0xF1, 0x39, 0xAB, 0x0D, 0x80,
             0x5F, 0xF7, 0x85, 0x87, 0xCC, 0xE6, 0xF1, 0xF2,
             0xCE, 0x39, 0x07, 0xBB, 0xDA, 0x5A, 0x67, 0x39,
             0xCF, 0x62, 0x47, 0x2C, 0xA2, 0x11, 0x85, 0x18,
             0xDA, 0xFE, 0x90, 0x7C, 0x4B, 0xEA, 0x88, 0xDC,
             0xAE, 0x39, 0x01, 0x07, 0x3A, 0xB6, 0xCC, 0x60,
             0xA5, 0x60, 0xC9, 0xA4, 0xD6, 0x33, 0x1E, 0x29,
             0xF8, 0x8A, 0xFE, 0xB9, 0x99, 0xA6, 0x4A, 0xE4,
             0xDB, 0xC7, 0xBF, 0x02, 0x22, 0xA9, 0xD4, 0x19,
             0x3A, 0x20, 0xE8, 0x1B, 0x40, 0x30, 0xF3, 0x28,
             0xE3, 0xA9, 0xCB, 0x7C, 0x92, 0x62, 0x04, 0x98,
             0x47, 0x4F, 0xCB, 0x64, 0xDA, 0xE1, 0xBB, 0xD7,
             0x9E, 0x4A, 0x9C, 0x04, 0x76, 0x47, 0x5E, 0xF0,
             0xF9, 0xAB, 0x5E, 0x89, 0xAE, 0x4D, 0x5A, 0xAE,
             0x9F, 0x87, 0x60, 0x21, 0xFA, 0x0B, 0xB2, 0x82,
             0x17, 0xCF, 0x27, 0x8D, 0x3A, 0xE9, 0xED, 0xDC,
             0x1C, 0x57, 0xBE, 0x5E, 0x17, 0xDC, 0x0D, 0x94,
             0x8E, 0x02, 0xFC, 0x05, 0xFE, 0xDF, 0x74, 0x07,
             0x05, 0xD8, 0xDC, 0xDC, 0x9D, 0x4B, 0x9C, 0xE6,
             0x80, 0x93, 0x65, 0x74, 0x94, 0x01, 0x5E, 0x05,
             0x17, 0x78, 0x96, 0xF1, 0x29, 0xFD, 0xFF, 0xB5,
             0xFF, 0x4A, 0xF5, 0x7C, 0x64, 0xD1, 0x51, 0xEC,
             0xEC, 0x8E, 0x74, 0x7B, 0x72, 0x67, 0xFA, 0x2D,
             0x8C, 0xF5, 0x97, 0x5E, 0x84, 0xC2, 0xEF, 0xAC,
             0x18, 0xDF, 0x16, 0xF2, 0xD8, 0x98, 0x0C, 0xE4,
             0x09, 0xC0, 0x3A, 0x1B, 0xC2, 0xB9, 0x5B, 0x34,
             0x34, 0x18, 0x98, 0xC6, 0xA5, 0xC6, 0x28, 0x54,
             0xB8, 0x53, 0x33, 0xE1, 0x4A, 0xA8, 0xE9 }

   DLP-4096 key in encoded form:

   -----BEGIN DSA PRIVATE KEY-----
   MIIGXgIBAAKCAf8x0lVfsuiJ8yCDeHla9IhbYtATWL3xF8C4rU0ivmLMkzRbbqj8
   VAtWj1CVu6CQPsXu2MauUl2ap+SZefCObE7b9WqTKQmga20eB1eVP5BbVVKZMV9C
   SPVLge9fBU2Ngk4SrquCSywvTF7eBGAw3DsWwoBZVoXKOMbnE9guTRv80z2H3iaV
   S6AFvEIXdzmyDx5GE4B57eWRZM5nI+NR5LL81Q1uq7RdqI+kzVYkiupEqi5BuP8o
   vTeIAIwu70vhkKCrXX2APJq+18e3dLUPqDgN1/4rPYSFo9iA71HVa0Efc+ZZ554L
   /zIUU1c+xQ2d1NCuyjCdOeQ4hieVA++UmFHj1Nxxq/OniGO5dcEGJMtRc0zbWCo6
   SMbXCEeDboCLDiJIuPqKjFWjV+gwVNZIssyluKOxaJGtUjVukoca9ZmlbpDJNDOl
   SlL9QuK+ZRXIzsNzlAcMJsrFyowmHS1QIYhruUxOmfp40lN8yvWhksnCr3egeDNF
   HxItqeb9e4OSEp7kmlYHXxo3BQBMBr02f7/LmgdKAuFlJSct+dMzy5GbW2EUB/f3
   pNnhHtKFpHWV6nQMv6Fr0vu4CtKl5jYER4CLHsUHWLhW9tykJdk2tJ7qW36qQHmj
   FT3tMhJ2TQAG8Ak2KEuW1ovJdP2vd7ZFeDY4xR6xGIqRcqA33knaSBqbAicB/zA2
   Bok/U75BEvlgGPmcz7lngn5JQDaYL68kBtJdi8xSSNsryxMCggH/GYkDGxK4g11m
   XJ9CMQUkoGSe7EwsSrqsrV1UjOD69T7KOGeq5hh9X2PA9mtW6ACtXQlYjKQlvOa9
   M5drusloY9HCbk9IJ2cFY/ucpRZcPJ8UHS59d6YRlVVNnOajJbk0Kl8K3gB+7Wnz
   LHhnjF8wLK+XYvzA1iLSv6X/cktZSSEcZi7T2BQer6u2KGXC8qZEpdw0DyQPc2FT
   PGVkzZ4ztljBOXHs2mYuHHm1iH6iRh41pror0CCA+OXGyL57+7ls9B8H1b3JZQC1
   bFNLcDaZVo9wC5rV7/we6L4vcDlQrNO4jCQ/gqLp9QHjh4ROd6qQLcDX2W6+TkvI
   s6sJZKwosVTNFTWkBlVAgzmOC+asmyb/mvTCzalVF1EVL71Mwtfxmp5/QaVuu+88
   1R32sQhIBhWo8+2Zn+x/DzxTh1UncHSzqA1LaoRxJuG53+I4lvWxl1ODmxin5mk+
   n7E9EVijq69OBGJ965YS2VlNMyYa5ZNn/8rew7Wv/8vf7UULU4vI2I0pjt0nszbo
   9e5tRh9XQDu0bbwEttkAx0hyjeePaI/NmpApTuqV585IKjmwYugE/Mtu99E1lLk1
   DsIPtQKoTE4wlsWQqiljeHkNgZ7CxQ3V9Ub14+TZaewz2kVSFNegXKr4h7Xomwnm
   ss8NVkPDhUgBiod7WhdyQCtLKfNciwKCAf8qSRFzGGURS4psb45AfVXDmrcQu0XK
   upTmsYWH0o+cbGlMAZoJsm9EjCozVaVnsaDIYYIuGcb63oxDqmHDvzm2leKidFUv
   6Fx2W4oe940bQpfvTDE/6NvyIhEwxe6R+ePTu/KcxHsbq68XnLqL1FupYdcKtr16
   oHX7KhUzFPw7LDuJhm5oLHqVjTt4h/DX2PQN9V5uUV0fu4h3jq+O8ejzEZp0mIBm
   fKjsxGv6ELrEZ0t3uU6w6Sp2psCBWdH0BrZoX+hbQajYBJORivUpmhxqET3i+XQn
   zYfEuigqZV1qTucVAS4MdQzDseXA8ivIKtI+tMDs9ICst9cxIVfbt+DlI3jp/0bu
   7wSvR08sTFXf/895i5A/SepD0GDvI+19Y4l7yy/xOasNgF/3hYfM5vHyzjkHu9pa
   ZznPYkcsohGFGNr+kHxL6ojcrjkBBzq2zGClYMmk1jMeKfiK/rmZpkrk28e/AiKp
   1Bk6IOgbQDDzKOOpy3ySYgSYR0/LZNrhu9eeSpwEdkde8PmrXomuTVqun4dgIfoL
   soIXzyeNOunt3BxXvl4X3A2UjgL8Bf7fdAcF2NzcnUuc5oCTZXSUAV4FF3iW8Sn9
   /7X/SvV8ZNFR7OyOdHtyZ/otjPWXXoTC76wY3xby2JgM5AnAOhvCuVs0NBiYxqXG
   KFS4UzPhSqjpAicBp3cRuJ1FUycpAboJWn/8FJyMBbAv3QQNyZiXEVvOw+YU8lV/
   nAw=
   -----END DSA PRIVATE KEY-----

2.3.  ECDLP Keys

   The following publicly known test keys may be used for ECDLP-based
   algorithms such as ECDSA and ECDH.

   P256 key "testECCP256":

           /* qx */
           256,
           { 0x42, 0x25, 0x48, 0xF8, 0x8F, 0xB7, 0x82, 0xFF,
             0xB5, 0xEC, 0xA3, 0x74, 0x44, 0x52, 0xC7, 0x2A,
             0x1E, 0x55, 0x8F, 0xBD, 0x6F, 0x73, 0xBE, 0x5E,
             0x48, 0xE9, 0x32, 0x32, 0xCC, 0x45, 0xC5, 0xB1 },
           /* qy */
           256,
           { 0x6C, 0x4C, 0xD1, 0x0C, 0x4C, 0xB8, 0xD5, 0xB8,
             0xA1, 0x71, 0x39, 0xE9, 0x48, 0x82, 0xC8, 0x99,
             0x25, 0x72, 0x99, 0x34, 0x25, 0xF4, 0x14, 0x19,
             0xAB, 0x7E, 0x90, 0xA4, 0x2A, 0x49, 0x42, 0x72 },
           /* d */
           256,
           { 0xE6, 0xCB, 0x5B, 0xDD, 0x80, 0xAA, 0x45, 0xAE,
             0x9C, 0x95, 0xE8, 0xC1, 0x54, 0x76, 0x67, 0x9F,
             0xFE, 0xC9, 0x53, 0xC1, 0x68, 0x51, 0xE7, 0x11,
             0xE7, 0x43, 0x93, 0x95, 0x89, 0xC6, 0x4F, 0xC1 }

   P256 key in encoded form:

   -----BEGIN EC PRIVATE KEY-----
   MHcCAQEEIObLW92AqkWunJXowVR2Z5/+yVPBaFHnEedDk5WJxk/BoAoGCCqGSM49
   AwEHoUQDQgAEQiVI+I+3gv+17KN0RFLHKh5Vj71vc75eSOkyMsxFxbFsTNEMTLjV
   uKFxOelIgsiZJXKZNCX0FBmrfpCkKklCcg==
   -----END EC PRIVATE KEY-----

   P384 key "testECCP384":

           /* qx */
           384,
           { 0x5B, 0x09, 0x01, 0xB8, 0x85, 0x23, 0x29, 0x6E,
             0xB9, 0x19, 0xD5, 0x0F, 0xFA, 0x1A, 0x9C, 0xB3,
             0x74, 0xBC, 0x4D, 0x40, 0x95, 0x86, 0x28, 0x2B,
             0xFE, 0xCA, 0x11, 0xB1, 0xD9, 0x5A, 0xDB, 0xB5,
             0x47, 0x34, 0xAF, 0x57, 0x0B, 0xF8, 0x2B, 0x72,
             0x28, 0xCF, 0x22, 0x6B, 0xCF, 0x4C, 0x25, 0xDD },
           /* qy */
           384,
           { 0xBC, 0xFE, 0x3B, 0x1A, 0x3A, 0xD3, 0x94, 0x30,
             0xEF, 0xF7, 0x63, 0xE1, 0xD6, 0x8D, 0x2E, 0x15,
             0x1D, 0x91, 0x72, 0x0B, 0x77, 0x95, 0xB5, 0x8D,
             0xA6, 0xB3, 0x46, 0x39, 0x61, 0x3A, 0x8F, 0xB9,
             0xB5, 0xA8, 0xDA, 0x48, 0xC6, 0x74, 0x71, 0x17,
             0xF9, 0x91, 0x9E, 0x84, 0x24, 0xF3, 0x7E, 0xC8 },
           /* d */
           384,
           { 0xE2, 0x56, 0x33, 0x28, 0xDF, 0xAB, 0xF6, 0x81,
             0x88, 0x60, 0x6B, 0x91, 0x32, 0x42, 0x81, 0xC1,
             0xD5, 0x8A, 0x44, 0x56, 0x43, 0x1B, 0x09, 0xD5,
             0x10, 0xB3, 0x5F, 0xEC, 0xC9, 0xF3, 0x07, 0xCA,
             0x18, 0x22, 0x84, 0x6F, 0xA2, 0x67, 0x13, 0x71,
             0xA9, 0xA8, 0x1B, 0xAC, 0x0E, 0x35, 0x74, 0x9D }

   P384 key in encoded form:

   -----BEGIN EC PRIVATE KEY-----
   MIGkAgEBBDDiVjMo36v2gYhga5EyQoHB1YpEVkMbCdUQs1/syfMHyhgihG+iZxNx
   qagbrA41dJ2gBwYFK4EEACKhZANiAARbCQG4hSMpbrkZ1Q/6GpyzdLxNQJWGKCv+
   yhGx2VrbtUc0r1cL+CtyKM8ia89MJd28/jsaOtOUMO/3Y+HWjS4VHZFyC3eVtY2m
   s0Y5YTqPubWo2kjGdHEX+ZGehCTzfsg=
   -----END EC PRIVATE KEY-----

   P521 key "testECCP521":

           /* qx */
           521,
           { 0x01, 0xD0, 0xFD, 0x72, 0x57, 0xA8, 0x4C, 0x74,
             0x7F, 0x56, 0x25, 0x75, 0xC0, 0x73, 0x85, 0xDB,
             0xEB, 0xF2, 0xF5, 0x2B, 0xEA, 0x58, 0x08, 0x3D,
             0xB8, 0x2F, 0xDD, 0x15, 0x31, 0xD8, 0xAA, 0xE3,
             0xCC, 0x87, 0x5F, 0xF0, 0x2F, 0xF7, 0xFA, 0x2D,
             0xA2, 0x60, 0xD8, 0xEB, 0x62, 0xD6, 0xD2, 0xF5,
             0xD6, 0x49, 0x27, 0x8E, 0x32, 0x17, 0x36, 0xA0,
             0x62, 0x8C, 0xBB, 0xB3, 0x03, 0x08, 0xB6, 0xE6,
             0x18, 0xDB },
           /* qy */
           521,
           { 0xF6, 0x2A, 0xD2, 0x04, 0xC6, 0x46, 0x03, 0x59,
             0xBC, 0x81, 0x8A, 0xB8, 0x96, 0x1B, 0xF0, 0xF0,
             0xFC, 0x0E, 0xC5, 0xAA, 0xE8, 0xA4, 0x28, 0x17,
             0x3C, 0xE5, 0x6F, 0x00, 0xDE, 0x9B, 0x15, 0x7C,
             0x1E, 0x5C, 0x82, 0xC6, 0x4F, 0x56, 0x2F, 0xCA,
             0xDE, 0xFC, 0x4A, 0x4C, 0x28, 0xF6, 0xD3, 0x42,
             0xCF, 0x3E, 0xF6, 0x16, 0xFC, 0x82, 0xD3, 0x3B,
             0x72, 0x85, 0xC9, 0x21, 0xF2, 0xBF, 0x36, 0xFD,
             0xD8 },
           /* d */
           521,
           { 0x01, 0xD9, 0x24, 0xDC, 0xCA, 0x0A, 0x88, 0x7F,
             0x8D, 0x99, 0x76, 0x7A, 0x37, 0xD8, 0x74, 0xE6,
             0x37, 0xA1, 0x2C, 0xCB, 0x47, 0x7D, 0x6E, 0x08,
             0x66, 0x53, 0x56, 0x69, 0x4D, 0x68, 0xB7, 0x65,
             0x5E, 0x50, 0x69, 0x63, 0x8F, 0xDE, 0x7B, 0x45,
             0xC8, 0x54, 0x01, 0x3D, 0xC7, 0x7A, 0x35, 0xB1,
             0x86, 0x55, 0xB8, 0x4C, 0x96, 0x6A, 0x60, 0x22,
             0x0D, 0x40, 0xF9, 0x1E, 0xD9, 0xF5, 0x14, 0x58,
             0x02, 0xEA }

   P521 key in encoded form:

   -----BEGIN EC PRIVATE KEY-----
   MIHcAgEBBEIB2STcygqIf42Zdno32HTmN6Esy0d9bghmU1ZpTWi3ZV5QaWOP3ntF
   yFQBPcd6NbGGVbhMlmpgIg1A+R7Z9RRYAuqgBwYFK4EEACOhgYkDgYYABAHQ/XJX
   qEx0f1YldcBzhdvr8vUr6lgIPbgv3RUx2KrjzIdf8C/3+i2iYNjrYtbS9dZJJ44y
   FzagYoy7swMItuYY2wD2KtIExkYDWbyBiriWG/Dw/A7FquikKBc85W8A3psVfB5c
   gsZPVi/K3vxKTCj200LPPvYW/ILTO3KFySHyvzb92A==
   -----END EC PRIVATE KEY-----

3.  IANA Considerations

   This document has no IANA actions.

4.  Security Considerations

   The intent of publishing known keys in this form is that they may be
   easily recognised as being test keys when encountered.  It should go
   without saying that these keys should never be used or relied upon in
   production environments.

   The authors await the inevitable Common Vulnerabilities and Exposures
   (CVEs).

Authors' Addresses

   Peter Gutmann
   University of Auckland
   Department of Computer Science
   Auckland
   New Zealand
   Email: pgut001@cs.auckland.ac.nz


   Corey Bonnell
   DigiCert
   Email: corey.bonnell@digicert.com