a1363d2ed9
ECDSA is unsafe to use if an entropy source produces predictable output for the ephemeral nonces. E.g., [Nguyen]. A simple countermeasure is to hash the secret key, the message, and entropy together to seed a CSPRNG, from which the ephemeral key is derived. Fixes #9452 -- This is a minimalist (in terms of patch size) solution, though not the most parsimonious in its use of primitives: - csprng_key = ChopMD-256(SHA2-512(priv.D||entropy||hash)) - reader = AES-256-CTR(k=csprng_key) This, however, provides at most 128-bit collision-resistance, so that Adv will have a term related to the number of messages signed that is significantly worse than plain ECDSA. This does not seem to be of any practical importance. ChopMD-256(SHA2-512(x)) is used, rather than SHA2-256(x), for two sets of reasons: *Practical:* SHA2-512 has a larger state and 16 more rounds; it is likely non-generically stronger than SHA2-256. And, AFAIK, cryptanalysis backs this up. (E.g., [Biryukov] gives a distinguisher on 47-round SHA2-256 with cost < 2^85.) This is well below a reasonable security-strength target. *Theoretical:* [Coron] and [Chang] show that Chop-MD(F(x)) is indifferentiable from a random oracle for slightly beyond the birthday barrier. It seems likely that this makes a generic security proof that this construction remains UF-CMA is possible in the indifferentiability framework. -- Many thanks to Payman Mohassel for reviewing this construction; any mistakes are mine, however. And, as he notes, reusing the private key in this way means that the generic-group (non-RO) proof of ECDSA's security given in [Brown] no longer directly applies. -- [Brown]: http://www.cacr.math.uwaterloo.ca/techreports/2000/corr2000-54.ps "Brown. The exact security of ECDSA. 2000" [Coron]: https://www.cs.nyu.edu/~puniya/papers/merkle.pdf "Coron et al. Merkle-Damgard revisited. 2005" [Chang]: https://www.iacr.org/archive/fse2008/50860436/50860436.pdf "Chang and Nandi. Improved indifferentiability security analysis of chopMD hash function. 2008" [Biryukov]: http://www.iacr.org/archive/asiacrypt2011/70730269/70730269.pdf "Biryukov et al. Second-order differential collisions for reduced SHA-256. 2011" [Nguyen]: ftp://ftp.di.ens.fr/pub/users/pnguyen/PubECDSA.ps "Nguyen and Shparlinski. The insecurity of the elliptic curve digital signature algorithm with partially known nonces. 2003" New tests: TestNonceSafety: Check that signatures are safe even with a broken entropy source. TestINDCCA: Check that signatures remain non-deterministic with a functional entropy source. Updated "golden" KATs in crypto/tls/testdata that use ECDSA suites. Change-Id: I55337a2fbec2e42a36ce719bd2184793682d678a Reviewed-on: https://go-review.googlesource.com/3340 Reviewed-by: Adam Langley <agl@golang.org>
86 lines
6.3 KiB
Plaintext
86 lines
6.3 KiB
Plaintext
>>> Flow 1 (client to server)
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00000000 16 03 01 00 7d 01 00 00 79 03 01 65 14 3f 40 e4 |....}...y..e.?@.|
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00000010 2f 74 65 7e d0 c8 87 03 59 61 9d c3 84 5e c9 62 |/te~....Ya...^.b|
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00000020 e6 46 b8 0c 4a 5e 3f 33 43 a5 dd 00 00 04 c0 0a |.F..J^?3C.......|
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00000030 00 ff 02 01 00 00 4b 00 0b 00 04 03 00 01 02 00 |......K.........|
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00000040 0a 00 3a 00 38 00 0e 00 0d 00 19 00 1c 00 0b 00 |..:.8...........|
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00000050 0c 00 1b 00 18 00 09 00 0a 00 1a 00 16 00 17 00 |................|
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00000060 08 00 06 00 07 00 14 00 15 00 04 00 05 00 12 00 |................|
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00000070 13 00 01 00 02 00 03 00 0f 00 10 00 11 00 0f 00 |................|
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00000080 01 01 |..|
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>>> Flow 2 (server to client)
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00000000 16 03 01 00 31 02 00 00 2d 03 01 00 00 00 00 00 |....1...-.......|
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00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
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00000020 00 00 00 00 00 00 00 00 00 00 00 00 c0 0a 00 00 |................|
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00000030 05 ff 01 00 01 00 16 03 01 02 0e 0b 00 02 0a 00 |................|
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00000040 02 07 00 02 04 30 82 02 00 30 82 01 62 02 09 00 |.....0...0..b...|
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00000050 b8 bf 2d 47 a0 d2 eb f4 30 09 06 07 2a 86 48 ce |..-G....0...*.H.|
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00000060 3d 04 01 30 45 31 0b 30 09 06 03 55 04 06 13 02 |=..0E1.0...U....|
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00000070 41 55 31 13 30 11 06 03 55 04 08 13 0a 53 6f 6d |AU1.0...U....Som|
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00000080 65 2d 53 74 61 74 65 31 21 30 1f 06 03 55 04 0a |e-State1!0...U..|
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00000090 13 18 49 6e 74 65 72 6e 65 74 20 57 69 64 67 69 |..Internet Widgi|
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000000a0 74 73 20 50 74 79 20 4c 74 64 30 1e 17 0d 31 32 |ts Pty Ltd0...12|
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000000b0 31 31 32 32 31 35 30 36 33 32 5a 17 0d 32 32 31 |1122150632Z..221|
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000000c0 31 32 30 31 35 30 36 33 32 5a 30 45 31 0b 30 09 |120150632Z0E1.0.|
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000000d0 06 03 55 04 06 13 02 41 55 31 13 30 11 06 03 55 |..U....AU1.0...U|
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000000e0 04 08 13 0a 53 6f 6d 65 2d 53 74 61 74 65 31 21 |....Some-State1!|
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000000f0 30 1f 06 03 55 04 0a 13 18 49 6e 74 65 72 6e 65 |0...U....Interne|
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00000100 74 20 57 69 64 67 69 74 73 20 50 74 79 20 4c 74 |t Widgits Pty Lt|
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00000110 64 30 81 9b 30 10 06 07 2a 86 48 ce 3d 02 01 06 |d0..0...*.H.=...|
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00000120 05 2b 81 04 00 23 03 81 86 00 04 00 c4 a1 ed be |.+...#..........|
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00000130 98 f9 0b 48 73 36 7e c3 16 56 11 22 f2 3d 53 c3 |...Hs6~..V.".=S.|
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00000140 3b 4d 21 3d cd 6b 75 e6 f6 b0 dc 9a df 26 c1 bc |;M!=.ku......&..|
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00000150 b2 87 f0 72 32 7c b3 64 2f 1c 90 bc ea 68 23 10 |...r2|.d/....h#.|
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00000160 7e fe e3 25 c0 48 3a 69 e0 28 6d d3 37 00 ef 04 |~..%.H:i.(m.7...|
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00000170 62 dd 0d a0 9c 70 62 83 d8 81 d3 64 31 aa 9e 97 |b....pb....d1...|
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00000180 31 bd 96 b0 68 c0 9b 23 de 76 64 3f 1a 5c 7f e9 |1...h..#.vd?.\..|
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00000190 12 0e 58 58 b6 5f 70 dd 9b d8 ea d5 d7 f5 d5 cc |..XX._p.........|
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000001a0 b9 b6 9f 30 66 5b 66 9a 20 e2 27 e5 bf fe 3b 30 |...0f[f. .'...;0|
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000001b0 09 06 07 2a 86 48 ce 3d 04 01 03 81 8c 00 30 81 |...*.H.=......0.|
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000001c0 88 02 42 01 88 a2 4f eb e2 45 c5 48 7d 1b ac f5 |..B...O..E.H}...|
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000001d0 ed 98 9d ae 47 70 c0 5e 1b b6 2f bd f1 b6 4d b7 |....Gp.^../...M.|
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000001e0 61 40 d3 11 a2 ce ee 0b 7e 92 7e ff 76 9d c3 3b |a@......~.~.v..;|
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000001f0 7e a5 3f ce fa 10 e2 59 ec 47 2d 7c ac da 4e 97 |~.?....Y.G-|..N.|
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00000200 0e 15 a0 6f d0 02 42 01 4d fc be 67 13 9c 2d 05 |...o..B.M..g..-.|
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00000210 0e bd 3f a3 8c 25 c1 33 13 83 0d 94 06 bb d4 37 |..?..%.3.......7|
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00000220 7a f6 ec 7a c9 86 2e dd d7 11 69 7f 85 7c 56 de |z..z......i..|V.|
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00000230 fb 31 78 2b e4 c7 78 0d ae cb be 9e 4e 36 24 31 |.1x+..x.....N6$1|
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00000240 7b 6a 0f 39 95 12 07 8f 2a 16 03 01 00 d6 0c 00 |{j.9....*.......|
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00000250 00 d2 03 00 17 41 04 1e 18 37 ef 0d 19 51 88 35 |.....A...7...Q.5|
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00000260 75 71 b5 e5 54 5b 12 2e 8f 09 67 fd a7 24 20 3e |uq..T[....g..$ >|
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00000270 b2 56 1c ce 97 28 5e f8 2b 2d 4f 9e f1 07 9f 6c |.V...(^.+-O....l|
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00000280 4b 5b 83 56 e2 32 42 e9 58 b6 d7 49 a6 b5 68 1a |K[.V.2B.X..I..h.|
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00000290 41 03 56 6b dc 5a 89 00 8b 30 81 88 02 42 01 3e |A.Vk.Z...0...B.>|
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000002a0 79 81 6e 89 cd 3e 3f ec e4 b5 75 17 28 ee fb 09 |y.n..>?...u.(...|
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000002b0 21 19 6f 3c e6 ca 1e f2 18 b6 47 f8 37 05 1c 85 |!.o<......G.7...|
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000002c0 0f a4 b8 6b 40 04 50 77 e3 05 9b 24 b8 93 e8 4d |...k@.Pw...$...M|
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000002d0 ef 30 cd 51 90 58 a2 49 71 b3 3f b9 46 ab a9 72 |.0.Q.X.Iq.?.F..r|
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000002e0 02 42 01 58 ef 20 c1 0a 33 f8 fd 50 9e 65 f5 ef |.B.X. ..3..P.e..|
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000002f0 f4 91 49 2d d2 de 66 2b 97 69 7d b1 d0 ef d6 91 |..I-..f+.i}.....|
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00000300 0f fc 57 2b 73 b9 49 01 33 d2 1b 5b 9a 2c 51 35 |..W+s.I.3..[.,Q5|
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00000310 0e eb 38 53 fa 20 07 84 52 b3 43 24 09 5a 32 c0 |..8S. ..R.C$.Z2.|
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00000320 32 17 34 6c 16 03 01 00 04 0e 00 00 00 |2.4l.........|
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>>> Flow 3 (client to server)
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00000000 16 03 01 00 46 10 00 00 42 41 04 31 74 f8 f6 18 |....F...BA.1t...|
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00000010 55 6a 9b 3b 78 0a 0e f0 c9 91 aa 8e 77 39 0a 88 |Uj.;x.......w9..|
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00000020 a4 d4 f6 04 9d de 89 18 b6 50 12 72 26 9c 8f e1 |.........P.r&...|
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00000030 f0 b2 e6 df ce 3b 46 be e9 2a 9a e3 7f d1 d5 92 |.....;F..*......|
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00000040 ff e3 ae 0a 2d a1 3b 07 f6 04 59 14 03 01 00 01 |....-.;...Y.....|
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00000050 01 16 03 01 00 30 02 4f df 41 30 97 6f f7 18 ca |.....0.O.A0.o...|
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00000060 05 35 17 a1 a2 a5 71 61 b1 d8 dd 9a c6 f3 54 53 |.5....qa......TS|
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00000070 84 f6 fb 93 1e 0e 9d e7 fe 35 85 9e 73 d0 2e a1 |.........5..s...|
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00000080 a7 63 d9 40 c6 ac |.c.@..|
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>>> Flow 4 (server to client)
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00000000 14 03 01 00 01 01 16 03 01 00 30 07 7e 4e 9c 19 |..........0.~N..|
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00000010 f0 35 cd 02 b7 a6 0a 1a b1 a8 11 a3 f9 b1 35 7b |.5............5{|
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00000020 96 7f e6 e1 00 c6 6d 9e e6 8a bb a2 b8 bd a3 9d |......m.........|
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00000030 05 22 1b f1 f5 28 4a 00 6e f1 71 17 03 01 00 20 |."...(J.n.q.... |
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00000040 ad c7 4c dc f4 81 1a 39 3d 86 5e 8e f5 0d a3 33 |..L....9=.^....3|
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00000050 88 32 e7 be 8b 6a 8d 44 29 7b 47 fd e5 33 01 1e |.2...j.D){G..3..|
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00000060 17 03 01 00 30 61 47 ee ae 89 25 ac 85 3b 8a 84 |....0aG...%..;..|
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00000070 47 61 ea 3e 4c 70 57 07 d6 f1 1c 21 cb 44 7e de |Ga.>LpW....!.D~.|
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00000080 b5 01 9e fb fe ad bc be 74 c0 65 a0 6b c1 0c 8c |........t.e.k...|
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00000090 2b 00 24 c6 b7 15 03 01 00 20 b7 8b 6b e5 77 ab |+.$...... ..k.w.|
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000000a0 f6 50 9e 88 4d 56 a8 25 8d 02 db cb 68 8b 3f 62 |.P..MV.%....h.?b|
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000000b0 be aa 02 24 75 b1 e5 4b 18 c9 |...$u..K..|
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