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crypto/ecdsa: make Sign safe with broken entropy sources

Browse source 
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]: 50860436.pdf
"Chang and Nandi. Improved indifferentiability security analysis
of chopMD hash function. 2008"

[Biryukov]: 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>
This commit is contained in:
David Leon Gil 2015-01-26 23:00:21 -08:00 • committed by Adam Langley
parent b180ba8f9b
commit 531f0d0055
9 changed files with 475 additions and 477 deletions
Download patch file Download diff file Expand all files Collapse all files

79
testdata/Server-TLSv10-ECDHE-ECDSA-AES vendored
View file

@ -1,12 +1,13 @@
>>> Flow 1 (client to server)
00000000 16 03 01 00 76 01 00 00 72 03 01 53 04 f0 f9 4b |....v...r..S...K|
00000010 30 a8 68 d0 79 13 14 69 ee 3b 5d 05 cb 71 63 43 |0.h.y..i.;]..qcC|
00000020 4a 55 6b 05 25 53 19 ba e0 2f b1 00 00 04 c0 0a |JUk.%S.../......|
00000030 00 ff 01 00 00 45 00 0b 00 04 03 00 01 02 00 0a |.....E..........|
00000040 00 34 00 32 00 0e 00 0d 00 19 00 0b 00 0c 00 18 |.4.2............|
00000050 00 09 00 0a 00 16 00 17 00 08 00 06 00 07 00 14 |................|
00000060 00 15 00 04 00 05 00 12 00 13 00 01 00 02 00 03 |................|
00000070 00 0f 00 10 00 11 00 0f 00 01 01 |...........|
00000000 16 03 01 00 7d 01 00 00 79 03 01 65 14 3f 40 e4 |....}...y..e.?@.|
00000010 2f 74 65 7e d0 c8 87 03 59 61 9d c3 84 5e c9 62 |/te~....Ya...^.b|
00000020 e6 46 b8 0c 4a 5e 3f 33 43 a5 dd 00 00 04 c0 0a |.F..J^?3C.......|
00000030 00 ff 02 01 00 00 4b 00 0b 00 04 03 00 01 02 00 |......K.........|
00000040 0a 00 3a 00 38 00 0e 00 0d 00 19 00 1c 00 0b 00 |..:.8...........|
00000050 0c 00 1b 00 18 00 09 00 0a 00 1a 00 16 00 17 00 |................|
00000060 08 00 06 00 07 00 14 00 15 00 04 00 05 00 12 00 |................|
00000070 13 00 01 00 02 00 03 00 0f 00 10 00 11 00 0f 00 |................|
00000080 01 01 |..|
>>> Flow 2 (server to client)
00000000 16 03 01 00 31 02 00 00 2d 03 01 00 00 00 00 00 |....1...-.......|
00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
@ -49,36 +50,36 @@
00000260 75 71 b5 e5 54 5b 12 2e 8f 09 67 fd a7 24 20 3e |uq..T[....g..$ >|
00000270 b2 56 1c ce 97 28 5e f8 2b 2d 4f 9e f1 07 9f 6c |.V...(^.+-O....l|
00000280 4b 5b 83 56 e2 32 42 e9 58 b6 d7 49 a6 b5 68 1a |K[.V.2B.X..I..h.|
00000290 41 03 56 6b dc 5a 89 00 8b 30 81 88 02 42 00 c6 |A.Vk.Z...0...B..|
000002a0 85 8e 06 b7 04 04 e9 cd 9e 3e cb 66 23 95 b4 42 |.........>.f#..B|
000002b0 9c 64 81 39 05 3f b5 21 f8 28 af 60 6b 4d 3d ba |.d.9.?.!.(.`kM=.|
000002c0 a1 4b 5e 77 ef e7 59 28 fe 1d c1 27 a2 ff a8 de |.K^w..Y(...'....|
000002d0 33 48 b3 c1 85 6a 42 9b f9 7e 7e 31 c2 e5 bd 66 |3H...jB..~~1...f|
000002e0 02 42 00 ad 7d 06 35 ab ec 8d ac d4 ba 1b 49 5e |.B..}.5.......I^|
000002f0 05 5f f0 97 93 82 b8 2b 8d 91 98 63 8e b4 14 62 |._.....+...c...b|
00000300 db 1e c9 2b 30 f8 41 9b a6 e6 bc de 0e 68 30 21 |...+0.A......h0!|
00000310 d8 ef 2f 05 42 da f2 e0 2c 06 33 1d 0d 9a 1a 75 |../.B...,.3....u|
00000320 59 a7 3a bc 16 03 01 00 04 0e 00 00 00 |Y.:..........|
00000290 41 03 56 6b dc 5a 89 00 8b 30 81 88 02 42 01 3e |A.Vk.Z...0...B.>|
000002a0 79 81 6e 89 cd 3e 3f ec e4 b5 75 17 28 ee fb 09 |y.n..>?...u.(...|
000002b0 21 19 6f 3c e6 ca 1e f2 18 b6 47 f8 37 05 1c 85 |!.o<......G.7...|
000002c0 0f a4 b8 6b 40 04 50 77 e3 05 9b 24 b8 93 e8 4d |...k@.Pw...$...M|
000002d0 ef 30 cd 51 90 58 a2 49 71 b3 3f b9 46 ab a9 72 |.0.Q.X.Iq.?.F..r|
000002e0 02 42 01 58 ef 20 c1 0a 33 f8 fd 50 9e 65 f5 ef |.B.X. ..3..P.e..|
000002f0 f4 91 49 2d d2 de 66 2b 97 69 7d b1 d0 ef d6 91 |..I-..f+.i}.....|
00000300 0f fc 57 2b 73 b9 49 01 33 d2 1b 5b 9a 2c 51 35 |..W+s.I.3..[.,Q5|
00000310 0e eb 38 53 fa 20 07 84 52 b3 43 24 09 5a 32 c0 |..8S. ..R.C$.Z2.|
00000320 32 17 34 6c 16 03 01 00 04 0e 00 00 00 |2.4l.........|
>>> Flow 3 (client to server)
00000000 16 03 01 00 46 10 00 00 42 41 04 08 28 cf bd 3c |....F...BA..(..<|
00000010 3c cc 98 9e 73 3f 92 a7 cb 22 83 3b c7 61 46 0e |<...s?...".;.aF.|
00000020 4d 7c 30 b5 06 85 2f 01 be b5 40 e2 64 1e 45 c1 |M|0.../...@.d.E.|
00000030 9d 73 95 d5 65 92 0b 9b e7 6f c6 91 ab b6 fa be |.s..e....o......|
00000040 61 83 a7 f2 eb f5 65 31 fe 24 7b 14 03 01 00 01 |a.....e1.${.....|
00000050 01 16 03 01 00 30 15 d1 c4 ca 0b 01 84 13 5a ba |.....0........Z.|
00000060 89 04 87 73 7c bb d8 89 7e 10 27 ba 6f 5d dc d3 |...s|...~.'.o]..|
00000070 b5 ef 32 86 58 cc fb eb 5c 32 9e 95 ef 01 1c ac |..2.X...\2......|
00000080 dc 8e df 7f fe 0a |......|
00000000 16 03 01 00 46 10 00 00 42 41 04 31 74 f8 f6 18 |....F...BA.1t...|
00000010 55 6a 9b 3b 78 0a 0e f0 c9 91 aa 8e 77 39 0a 88 |Uj.;x.......w9..|
00000020 a4 d4 f6 04 9d de 89 18 b6 50 12 72 26 9c 8f e1 |.........P.r&...|
00000030 f0 b2 e6 df ce 3b 46 be e9 2a 9a e3 7f d1 d5 92 |.....;F..*......|
00000040 ff e3 ae 0a 2d a1 3b 07 f6 04 59 14 03 01 00 01 |....-.;...Y.....|
00000050 01 16 03 01 00 30 02 4f df 41 30 97 6f f7 18 ca |.....0.O.A0.o...|
00000060 05 35 17 a1 a2 a5 71 61 b1 d8 dd 9a c6 f3 54 53 |.5....qa......TS|
00000070 84 f6 fb 93 1e 0e 9d e7 fe 35 85 9e 73 d0 2e a1 |.........5..s...|
00000080 a7 63 d9 40 c6 ac |.c.@..|
>>> Flow 4 (server to client)
00000000 14 03 01 00 01 01 16 03 01 00 30 e8 48 86 81 3c |..........0.H..<|
00000010 f5 25 5c 94 a9 06 c4 5c 71 62 b1 43 76 ec 2c 44 |.%\....\qb.Cv.,D|
00000020 95 b5 8c 95 d2 ff 82 92 b6 fc 52 75 03 c6 a1 f0 |..........Ru....|
00000030 99 6d b1 ed ec 68 6c d7 9f 18 50 17 03 01 00 20 |.m...hl...P.... |
00000040 32 d9 26 8a 81 b8 9d a5 7b fd d5 4e 7a db 2e 29 |2.&.....{..Nz..)|
00000050 58 9a 4f 6a 27 18 bc dc c2 49 b8 65 cb 8e 16 5a |X.Oj'....I.e...Z|
00000060 17 03 01 00 30 c4 56 0a ad 9a 82 cb 3e 32 f1 7c |....0.V.....>2.||
00000070 95 6e dd cd e9 4d f0 e5 2d c9 a3 f7 de bb d7 fd |.n...M..-.......|
00000080 84 bb df 34 8c 64 1f 03 58 64 19 4a 5b 7a a8 81 |...4.d..Xd.J[z..|
00000090 52 bb 51 0a 43 15 03 01 00 20 89 18 7a 40 ec 49 |R.Q.C.... ..z@.I|
000000a0 52 d5 d3 20 ac 07 eb e9 4a 78 23 cf e7 21 32 74 |R.. ....Jx#..!2t|
000000b0 ec 40 8d a8 f4 33 1c ae 93 cf |.@...3....|
00000000 14 03 01 00 01 01 16 03 01 00 30 07 7e 4e 9c 19 |..........0.~N..|
00000010 f0 35 cd 02 b7 a6 0a 1a b1 a8 11 a3 f9 b1 35 7b |.5............5{|
00000020 96 7f e6 e1 00 c6 6d 9e e6 8a bb a2 b8 bd a3 9d |......m.........|
00000030 05 22 1b f1 f5 28 4a 00 6e f1 71 17 03 01 00 20 |."...(J.n.q.... |
00000040 ad c7 4c dc f4 81 1a 39 3d 86 5e 8e f5 0d a3 33 |..L....9=.^....3|
00000050 88 32 e7 be 8b 6a 8d 44 29 7b 47 fd e5 33 01 1e |.2...j.D){G..3..|
00000060 17 03 01 00 30 61 47 ee ae 89 25 ac 85 3b 8a 84 |....0aG...%..;..|
00000070 47 61 ea 3e 4c 70 57 07 d6 f1 1c 21 cb 44 7e de |Ga.>LpW....!.D~.|
00000080 b5 01 9e fb fe ad bc be 74 c0 65 a0 6b c1 0c 8c |........t.e.k...|
00000090 2b 00 24 c6 b7 15 03 01 00 20 b7 8b 6b e5 77 ab |+.$...... ..k.w.|
000000a0 f6 50 9e 88 4d 56 a8 25 8d 02 db cb 68 8b 3f 62 |.P..MV.%....h.?b|
000000b0 be aa 02 24 75 b1 e5 4b 18 c9 |...$u..K..|