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>
65 lines
4.8 KiB
Plaintext
65 lines
4.8 KiB
Plaintext
>>> Flow 1 (client to server)
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00000000 16 03 01 00 75 01 00 00 71 03 03 00 00 00 00 00 |....u...q.......|
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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 00 1a c0 2f |.............../|
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00000030 c0 2b c0 11 c0 07 c0 13 c0 09 c0 14 c0 0a 00 05 |.+..............|
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00000040 00 2f 00 35 c0 12 00 0a 01 00 00 2e 00 05 00 05 |./.5............|
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00000050 01 00 00 00 00 00 0a 00 08 00 06 00 17 00 18 00 |................|
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00000060 19 00 0b 00 02 01 00 00 0d 00 0a 00 08 04 01 04 |................|
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00000070 03 02 01 02 03 ff 01 00 01 00 |..........|
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>>> Flow 2 (server to client)
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00000000 16 03 01 00 51 02 00 00 4d 03 01 54 c7 34 52 b0 |....Q...M..T.4R.|
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00000010 47 c3 7d 3d 1f 16 7f 5c 8c 6e 05 0a d5 85 19 2a |G.}=...\.n.....*|
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00000020 9a d3 1e 8f dc ed 92 53 fd dd 40 20 af 90 44 e7 |.......S..@ ..D.|
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00000030 2d 28 15 7e 45 50 0c b6 a6 15 a7 cf 99 19 85 a8 |-(.~EP..........|
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00000040 1b df 61 c1 d5 7e 51 e6 80 d4 75 66 c0 09 00 00 |..a..~Q...uf....|
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00000050 05 ff 01 00 01 00 16 03 01 02 0e 0b 00 02 0a 00 |................|
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00000060 02 07 00 02 04 30 82 02 00 30 82 01 62 02 09 00 |.....0...0..b...|
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00000070 b8 bf 2d 47 a0 d2 eb f4 30 09 06 07 2a 86 48 ce |..-G....0...*.H.|
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00000080 3d 04 01 30 45 31 0b 30 09 06 03 55 04 06 13 02 |=..0E1.0...U....|
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00000090 41 55 31 13 30 11 06 03 55 04 08 13 0a 53 6f 6d |AU1.0...U....Som|
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000000a0 65 2d 53 74 61 74 65 31 21 30 1f 06 03 55 04 0a |e-State1!0...U..|
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000000b0 13 18 49 6e 74 65 72 6e 65 74 20 57 69 64 67 69 |..Internet Widgi|
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000000c0 74 73 20 50 74 79 20 4c 74 64 30 1e 17 0d 31 32 |ts Pty Ltd0...12|
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000000d0 31 31 32 32 31 35 30 36 33 32 5a 17 0d 32 32 31 |1122150632Z..221|
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000000e0 31 32 30 31 35 30 36 33 32 5a 30 45 31 0b 30 09 |120150632Z0E1.0.|
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000000f0 06 03 55 04 06 13 02 41 55 31 13 30 11 06 03 55 |..U....AU1.0...U|
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00000100 04 08 13 0a 53 6f 6d 65 2d 53 74 61 74 65 31 21 |....Some-State1!|
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00000110 30 1f 06 03 55 04 0a 13 18 49 6e 74 65 72 6e 65 |0...U....Interne|
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00000120 74 20 57 69 64 67 69 74 73 20 50 74 79 20 4c 74 |t Widgits Pty Lt|
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00000130 64 30 81 9b 30 10 06 07 2a 86 48 ce 3d 02 01 06 |d0..0...*.H.=...|
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00000140 05 2b 81 04 00 23 03 81 86 00 04 00 c4 a1 ed be |.+...#..........|
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00000150 98 f9 0b 48 73 36 7e c3 16 56 11 22 f2 3d 53 c3 |...Hs6~..V.".=S.|
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00000160 3b 4d 21 3d cd 6b 75 e6 f6 b0 dc 9a df 26 c1 bc |;M!=.ku......&..|
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00000170 b2 87 f0 72 32 7c b3 64 2f 1c 90 bc ea 68 23 10 |...r2|.d/....h#.|
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00000180 7e fe e3 25 c0 48 3a 69 e0 28 6d d3 37 00 ef 04 |~..%.H:i.(m.7...|
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00000190 62 dd 0d a0 9c 70 62 83 d8 81 d3 64 31 aa 9e 97 |b....pb....d1...|
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000001a0 31 bd 96 b0 68 c0 9b 23 de 76 64 3f 1a 5c 7f e9 |1...h..#.vd?.\..|
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000001b0 12 0e 58 58 b6 5f 70 dd 9b d8 ea d5 d7 f5 d5 cc |..XX._p.........|
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000001c0 b9 b6 9f 30 66 5b 66 9a 20 e2 27 e5 bf fe 3b 30 |...0f[f. .'...;0|
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000001d0 09 06 07 2a 86 48 ce 3d 04 01 03 81 8c 00 30 81 |...*.H.=......0.|
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000001e0 88 02 42 01 88 a2 4f eb e2 45 c5 48 7d 1b ac f5 |..B...O..E.H}...|
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000001f0 ed 98 9d ae 47 70 c0 5e 1b b6 2f bd f1 b6 4d b7 |....Gp.^../...M.|
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00000200 61 40 d3 11 a2 ce ee 0b 7e 92 7e ff 76 9d c3 3b |a@......~.~.v..;|
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00000210 7e a5 3f ce fa 10 e2 59 ec 47 2d 7c ac da 4e 97 |~.?....Y.G-|..N.|
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00000220 0e 15 a0 6f d0 02 42 01 4d fc be 67 13 9c 2d 05 |...o..B.M..g..-.|
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00000230 0e bd 3f a3 8c 25 c1 33 13 83 0d 94 06 bb d4 37 |..?..%.3.......7|
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00000240 7a f6 ec 7a c9 86 2e dd d7 11 69 7f 85 7c 56 de |z..z......i..|V.|
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00000250 fb 31 78 2b e4 c7 78 0d ae cb be 9e 4e 36 24 31 |.1x+..x.....N6$1|
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00000260 7b 6a 0f 39 95 12 07 8f 2a 16 03 01 00 c0 0c 00 |{j.9....*.......|
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00000270 00 bc 03 00 03 2b 04 02 35 e1 56 0b 72 c9 4b e8 |.....+..5.V.r.K.|
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00000280 69 29 75 1d ff a3 f4 06 73 72 f2 e2 07 2e 9e 66 |i)u.....sr.....f|
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00000290 73 7b 7f 62 b1 ed 0d 84 2b d7 d7 32 22 25 92 4c |s{.b....+..2"%.L|
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000002a0 d9 00 8b 30 81 88 02 42 01 23 24 db 0a d5 ab e5 |...0...B.#$.....|
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000002b0 a7 11 31 ce fb 36 89 54 8c d1 65 14 bc a2 5c 42 |..1..6.T..e...\B|
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000002c0 08 c9 a2 6f 24 b2 f2 aa bc 02 5c 44 98 2d 95 91 |...o$.....\D.-..|
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000002d0 98 22 69 fc c3 52 c5 60 ca f2 9c 67 ce 96 2b bf |."i..R.`...g..+.|
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000002e0 66 73 d5 ac 96 bf 0f 92 6d 1d 02 42 00 a6 7d 0d |fs......m..B..}.|
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000002f0 c9 78 f6 35 7b 19 9c 25 82 48 52 9c 11 b7 06 5b |.x.5{..%.HR....[|
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00000300 f8 a7 30 cd ee bf 37 af 23 f2 06 23 d9 77 da 76 |..0...7.#..#.w.v|
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00000310 12 2a da f9 34 1f f0 4f f9 94 2e 4d e6 c4 eb bb |.*..4..O...M....|
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00000320 b2 55 23 70 ae 55 de a5 68 bd a6 a4 d7 c4 16 03 |.U#p.U..h.......|
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00000330 01 00 04 0e 00 00 00 |.......|
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>>> Flow 3 (client to server)
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00000000 15 03 01 00 02 02 0a |.......|
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