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authorThomas Voss <mail@thomasvoss.com> 2024-11-27 20:54:24 +0100
committerThomas Voss <mail@thomasvoss.com> 2024-11-27 20:54:24 +0100
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+Network Working Group T. Kivinen
+Request for Comments: 3526 M. Kojo
+Category: Standards Track SSH Communications Security
+ May 2003
+
+
+ More Modular Exponential (MODP) Diffie-Hellman groups
+ for Internet Key Exchange (IKE)
+
+Status of this Memo
+
+ This document specifies an Internet standards track protocol for the
+ Internet community, and requests discussion and suggestions for
+ improvements. Please refer to the current edition of the "Internet
+ Official Protocol Standards" (STD 1) for the standardization state
+ and status of this protocol. Distribution of this memo is unlimited.
+
+Copyright Notice
+
+ Copyright (C) The Internet Society (2003). All Rights Reserved.
+
+Abstract
+
+ This document defines new Modular Exponential (MODP) Groups for the
+ Internet Key Exchange (IKE) protocol. It documents the well known
+ and used 1536 bit group 5, and also defines new 2048, 3072, 4096,
+ 6144, and 8192 bit Diffie-Hellman groups numbered starting at 14.
+ The selection of the primes for theses groups follows the criteria
+ established by Richard Schroeppel.
+
+Table of Contents
+
+ 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . 2
+ 2. 1536-bit MODP Group . . . . . . . . . . . . . . . . . . . 3
+ 3. 2048-bit MODP Group . . . . . . . . . . . . . . . . . . . 3
+ 4. 3072-bit MODP Group . . . . . . . . . . . . . . . . . . . 4
+ 5. 4096-bit MODP Group . . . . . . . . . . . . . . . . . . . 5
+ 6. 6144-bit MODP Group . . . . . . . . . . . . . . . . . . . 6
+ 7. 8192-bit MODP Group . . . . . . . . . . . . . . . . . . . 6
+ 8. Security Considerations . . . . . . . . . . . . . . . . . 8
+ 9. IANA Considerations . . . . . . . . . . . . . . . . . . . 8
+ 10. Normative References. . . . . . . . . . . . . . . . . . . 8
+ 11. Non-Normative References. . . . . . . . . . . . . . . . . 8
+ 12. Authors' Addresses . . . . . . . . . . . . . . . . . . . 9
+ 13. Full Copyright Statement. . . . . . . . . . . . . . . . . 10
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 1]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+1. Introduction
+
+ One of the important protocol parameters negotiated by Internet Key
+ Exchange (IKE) [RFC-2409] is the Diffie-Hellman "group" that will be
+ used for certain cryptographic operations. IKE currently defines 4
+ groups. These groups are approximately as strong as a symmetric key
+ of 70-80 bits.
+
+ The new Advanced Encryption Standard (AES) cipher [AES], which has
+ more strength, needs stronger groups. For the 128-bit AES we need
+ about a 3200-bit group [Orman01]. The 192 and 256-bit keys would
+ need groups that are about 8000 and 15400 bits respectively. Another
+ source [RSA13] [Rousseau00] estimates that the security equivalent
+ key size for the 192-bit symmetric cipher is 2500 bits instead of
+ 8000 bits, and the equivalent key size 256-bit symmetric cipher is
+ 4200 bits instead of 15400 bits.
+
+ Because of this disagreement, we just specify different groups
+ without specifying which group should be used with 128, 192 or 256-
+ bit AES. With current hardware groups bigger than 8192-bits being
+ too slow for practical use, this document does not provide any groups
+ bigger than 8192-bits.
+
+ The exponent size used in the Diffie-Hellman must be selected so that
+ it matches other parts of the system. It should not be the weakest
+ link in the security system. It should have double the entropy of
+ the strength of the entire system, i.e., if you use a group whose
+ strength is 128 bits, you must use more than 256 bits of randomness
+ in the exponent used in the Diffie-Hellman calculation.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 2]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+2. 1536-bit MODP Group
+
+ The 1536 bit MODP group has been used for the implementations for
+ quite a long time, but was not defined in RFC 2409 (IKE).
+ Implementations have been using group 5 to designate this group, we
+ standardize that practice here.
+
+ The prime is: 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }
+
+ Its hexadecimal value is:
+
+ FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
+ 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
+ EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
+ E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
+ EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
+ C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
+ 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+ 670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF
+
+ The generator is: 2.
+
+3. 2048-bit MODP Group
+
+ This group is assigned id 14.
+
+ This prime is: 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }
+
+ Its hexadecimal value is:
+
+ FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
+ 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
+ EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
+ E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
+ EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
+ C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
+ 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+ 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
+ E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
+ DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
+ 15728E5A 8AACAA68 FFFFFFFF FFFFFFFF
+
+ The generator is: 2.
+
+
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 3]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+4. 3072-bit MODP Group
+
+ This group is assigned id 15.
+
+ This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 }
+
+ Its hexadecimal value is:
+
+ FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
+ 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
+ EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
+ E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
+ EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
+ C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
+ 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+ 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
+ E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
+ DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
+ 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
+ ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
+ ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
+ F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
+ BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
+ 43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
+
+ The generator is: 2.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 4]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+5. 4096-bit MODP Group
+
+ This group is assigned id 16.
+
+ This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 }
+
+ Its hexadecimal value is:
+
+ FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
+ 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
+ EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
+ E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
+ EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
+ C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
+ 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+ 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
+ E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
+ DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
+ 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
+ ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
+ ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
+ F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
+ BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
+ 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
+ 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
+ 2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
+ 287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
+ 1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
+ 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
+ FFFFFFFF FFFFFFFF
+
+ The generator is: 2.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 5]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+6. 6144-bit MODP Group
+
+ This group is assigned id 17.
+
+ This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 }
+
+ Its hexadecimal value is:
+
+ FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
+ 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
+ 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
+ A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
+ 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
+ FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+ 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
+ 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
+ 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
+ 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
+ B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
+ 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
+ BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
+ E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
+ 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
+ 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
+ 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
+ D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
+ 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
+ AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
+ DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
+ 2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
+ F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
+ BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
+ CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
+ B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
+ 387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
+ 6DCC4024 FFFFFFFF FFFFFFFF
+
+ The generator is: 2.
+
+7. 8192-bit MODP Group
+
+ This group is assigned id 18.
+
+ This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 }
+
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 6]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+ Its hexadecimal value is:
+
+ FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
+ 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
+ EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
+ E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
+ EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
+ C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
+ 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+ 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
+ E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
+ DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
+ 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
+ ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
+ ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
+ F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
+ BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
+ 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
+ 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
+ 2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
+ 287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
+ 1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
+ 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
+ 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD
+ F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831
+ 179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
+ DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF
+ 5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6
+ D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3
+ 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
+ CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328
+ 06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
+ DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE
+ 12BF2D5B 0B7474D6 E694F91E 6DBE1159 74A3926F 12FEE5E4
+ 38777CB6 A932DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
+ 741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C 5AE4F568
+ 3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
+ 22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B
+ 4BCBC886 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A
+ 062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
+ 4597E899 A0255DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
+ B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92
+ 4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47
+ 9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
+ 60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
+
+ The generator is: 2.
+
+
+
+
+Kivinen & Kojo Standards Track [Page 7]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+8. Security Considerations
+
+ This document describes new stronger groups to be used in IKE. The
+ strengths of the groups defined here are always estimates and there
+ are as many methods to estimate them as there are cryptographers.
+ For the strength estimates below we took the both ends of the scale
+ so the actual strength estimate is likely between the two numbers
+ given here.
+
+ +--------+----------+---------------------+---------------------+
+ | Group | Modulus | Strength Estimate 1 | Strength Estimate 2 |
+ | | +----------+----------+----------+----------+
+ | | | | exponent | | exponent |
+ | | | in bits | size | in bits | size |
+ +--------+----------+----------+----------+----------+----------+
+ | 5 | 1536-bit | 90 | 180- | 120 | 240- |
+ | 14 | 2048-bit | 110 | 220- | 160 | 320- |
+ | 15 | 3072-bit | 130 | 260- | 210 | 420- |
+ | 16 | 4096-bit | 150 | 300- | 240 | 480- |
+ | 17 | 6144-bit | 170 | 340- | 270 | 540- |
+ | 18 | 8192-bit | 190 | 380- | 310 | 620- |
+ +--------+----------+---------------------+---------------------+
+
+9. IANA Considerations
+
+ IKE [RFC-2409] defines 4 Diffie-Hellman Groups, numbered 1 through 4.
+
+ This document defines a new group 5, and new groups from 14 to 18.
+ Requests for additional assignment are via "IETF Consensus" as
+ defined in RFC 2434 [RFC-2434]. Specifically, new groups are
+ expected to be documented in a Standards Track RFC.
+
+10. Normative References
+
+ [RFC-2409] Harkins, D. and D. Carrel, "The Internet Key Exchange
+ (IKE)", RFC 2409, November 1998.
+
+ [RFC-2434] Narten, T. and H. Alvestrand, "Guidelines for Writing an
+ IANA Considerations Section in RFCs", BCP 26, RFC 2434,
+ October 1998.
+
+11. Non-Normative References
+
+ [AES] NIST, FIPS PUB 197, "Advanced Encryption Standard
+ (AES)," November 2001.
+ http://csrc.nist.gov/publications/fips/fips197/fips-
+ 197.{ps,pdf}
+
+
+
+
+Kivinen & Kojo Standards Track [Page 8]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+ [RFC-2412] Orman, H., "The OAKLEY Key Determination Protocol", RFC
+ 2412, November 1998.
+
+ [Orman01] Orman, H. and P. Hoffman, "Determining Strengths For
+ Public Keys Used For Exchanging Symmetric Keys", Work in
+ progress.
+
+ [RSA13] Silverman, R. "RSA Bulleting #13: A Cost-Based Security
+ Analysis of Symmetric and Asymmetric Key Lengths", April
+ 2000, http://www.rsasecurity.com/rsalabs/bulletins/
+ bulletin13.html
+
+ [Rousseau00] Rousseau, F. "New Time and Space Based Key Size
+ Equivalents for RSA and Diffie-Hellman", December 2000,
+ http://www.sandelman.ottawa.on.ca/ipsec/2000/12/
+ msg00045.html
+
+12. Authors' Addresses
+
+ Tero Kivinen
+ SSH Communications Security Corp
+ Fredrikinkatu 42
+ FIN-00100 HELSINKI
+ Finland
+
+ EMail: kivinen@ssh.fi
+
+
+ Mika Kojo
+ HELSINKI
+ Finland
+
+ EMail: mika.kojo@helsinki.fi
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Kivinen & Kojo Standards Track [Page 9]
+
+RFC 3526 MODP Diffie-Hellman groups for IKE May 2003
+
+
+13. Full Copyright Statement
+
+ Copyright (C) The Internet Society (2003). All Rights Reserved.
+
+ This document and translations of it may be copied and furnished to
+ others, and derivative works that comment on or otherwise explain it
+ or assist in its implementation may be prepared, copied, published
+ and distributed, in whole or in part, without restriction of any
+ kind, provided that the above copyright notice and this paragraph are
+ included on all such copies and derivative works. However, this
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+Kivinen & Kojo Standards Track [Page 10]
+