2013-12-20 16:37:05 +00:00
|
|
|
>>> Flow 1 (client to server)
|
crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +00:00
|
|
|
00000000 16 03 01 01 61 01 00 01 5d 03 03 47 c5 84 0f 55 |....a...]..G...U|
|
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|
|
|
00000010 83 4d 4a 1c 48 51 15 e4 74 72 84 70 2f 24 e9 ab |.MJ.HQ..tr.p/$..|
|
|
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|
00000020 42 1e 01 e1 85 27 2f b5 c1 43 14 00 00 c4 c0 30 |B....'/..C.....0|
|
|
|
|
|
00000030 c0 2c c0 28 c0 24 c0 14 c0 0a 00 a5 00 a3 00 a1 |.,.(.$..........|
|
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|
|
00000040 00 9f 00 6b 00 6a 00 69 00 68 00 39 00 38 00 37 |...k.j.i.h.9.8.7|
|
|
|
|
|
00000050 00 36 00 88 00 87 00 86 00 85 c0 32 c0 2e c0 2a |.6.........2...*|
|
|
|
|
|
00000060 c0 26 c0 0f c0 05 00 9d 00 3d 00 35 00 84 c0 2f |.&.......=.5.../|
|
|
|
|
|
00000070 c0 2b c0 27 c0 23 c0 13 c0 09 00 a4 00 a2 00 a0 |.+.'.#..........|
|
|
|
|
|
00000080 00 9e 00 67 00 40 00 3f 00 3e 00 33 00 32 00 31 |...g.@.?.>.3.2.1|
|
|
|
|
|
00000090 00 30 00 9a 00 99 00 98 00 97 00 45 00 44 00 43 |.0.........E.D.C|
|
|
|
|
|
000000a0 00 42 c0 31 c0 2d c0 29 c0 25 c0 0e c0 04 00 9c |.B.1.-.).%......|
|
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|
|
000000b0 00 3c 00 2f 00 96 00 41 00 07 c0 11 c0 07 c0 0c |.<./...A........|
|
|
|
|
|
000000c0 c0 02 00 05 00 04 c0 12 c0 08 00 16 00 13 00 10 |................|
|
|
|
|
|
000000d0 00 0d c0 0d c0 03 00 0a 00 15 00 12 00 0f 00 0c |................|
|
|
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|
|
000000e0 00 09 00 14 00 11 00 0e 00 0b 00 08 00 06 00 03 |................|
|
|
|
|
|
000000f0 00 ff 02 01 00 00 6f 00 0b 00 04 03 00 01 02 00 |......o.........|
|
|
|
|
|
00000100 0a 00 3a 00 38 00 0e 00 0d 00 19 00 1c 00 0b 00 |..:.8...........|
|
|
|
|
|
00000110 0c 00 1b 00 18 00 09 00 0a 00 1a 00 16 00 17 00 |................|
|
|
|
|
|
00000120 08 00 06 00 07 00 14 00 15 00 04 00 05 00 12 00 |................|
|
|
|
|
|
00000130 13 00 01 00 02 00 03 00 0f 00 10 00 11 00 0d 00 |................|
|
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|
00000140 20 00 1e 06 01 06 02 06 03 05 01 05 02 05 03 04 | ...............|
|
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00000150 01 04 02 04 03 03 01 03 02 03 03 02 01 02 02 02 |................|
|
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|
00000160 03 00 0f 00 01 01 |......|
|
2013-12-20 16:37:05 +00:00
|
|
|
>>> Flow 2 (server to client)
|
crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +00:00
|
|
|
00000000 16 03 03 00 31 02 00 00 2d 03 03 00 00 00 00 00 |....1...-.......|
|
2013-12-20 16:37:05 +00:00
|
|
|
00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
|
crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +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 03 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..-.|
|
|
|
|
|
00000210 0e bd 3f a3 8c 25 c1 33 13 83 0d 94 06 bb d4 37 |..?..%.3.......7|
|
|
|
|
|
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$1|
|
|
|
|
|
00000240 7b 6a 0f 39 95 12 07 8f 2a 16 03 03 00 d7 0c 00 |{j.9....*.......|
|
|
|
|
|
00000250 00 d3 03 00 17 41 04 1e 18 37 ef 0d 19 51 88 35 |.....A...7...Q.5|
|
|
|
|
|
00000260 75 71 b5 e5 54 5b 12 2e 8f 09 67 fd a7 24 20 3e |uq..T[....g..$ >|
|
|
|
|
|
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 04 03 00 8a 30 81 87 02 42 |A.Vk.Z.....0...B|
|
|
|
|
|
000002a0 00 e5 db 39 b2 73 2b 4b 19 66 d6 d6 de d2 ed ae |...9.s+K.f......|
|
|
|
|
|
000002b0 0c ac 74 96 12 b2 e0 87 73 7c 63 18 8c 58 3f 56 |..t.....s|c..X?V|
|
|
|
|
|
000002c0 4c fe 0f a5 2d b9 b8 1c 7d 4d 49 b9 ca f0 52 01 |L...-...}MI...R.|
|
|
|
|
|
000002d0 12 e2 a9 54 9f 4d ab b7 93 71 3c 1b 96 b0 87 8b |...T.M...q<.....|
|
|
|
|
|
000002e0 87 c3 02 41 79 c3 50 88 2f 9a b8 a3 f0 14 63 ee |...Ay.P./.....c.|
|
|
|
|
|
000002f0 d6 76 dd d4 1d 1c ce 4c ba 53 40 ac 01 d9 62 a7 |.v.....L.S@...b.|
|
|
|
|
|
00000300 bc ee 66 67 fc da f4 b3 0f fd 50 5d 31 0e 2d 41 |..fg......P]1.-A|
|
|
|
|
|
00000310 64 d5 51 30 a3 0e ee 20 f9 9d 0e 11 df 68 a6 f4 |d.Q0... .....h..|
|
|
|
|
|
00000320 54 d4 54 7a 05 16 03 03 00 04 0e 00 00 00 |T.Tz..........|
|
2013-12-20 16:37:05 +00:00
|
|
|
>>> Flow 3 (client to server)
|
crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +00:00
|
|
|
00000000 16 03 03 00 46 10 00 00 42 41 04 00 a1 de 66 1d |....F...BA....f.|
|
|
|
|
|
00000010 05 57 3b d2 0e 5f ba 4d e9 b7 93 0a 3e bd 25 98 |.W;.._.M....>.%.|
|
|
|
|
|
00000020 76 a4 8a c9 d3 c8 04 85 f6 8d 4f 3e 32 4c 25 cb |v.........O>2L%.|
|
|
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|
|
00000030 b5 57 86 b5 04 9d f6 ba f3 17 c8 43 cb eb 8b d0 |.W.........C....|
|
|
|
|
|
00000040 ed 99 23 c7 4d 63 95 e2 cd 52 ba 14 03 03 00 01 |..#.Mc...R......|
|
|
|
|
|
00000050 01 16 03 03 00 40 33 b4 f5 4a 64 88 ef dc b6 e5 |.....@3..Jd.....|
|
|
|
|
|
00000060 b6 1e 40 3e 64 5a 2c 11 97 69 4c b6 7a 4c 9a 8a |..@>dZ,..iL.zL..|
|
|
|
|
|
00000070 71 f2 60 e9 39 db 96 2a a3 33 1b 7f 43 15 8b 99 |q.`.9..*.3..C...|
|
|
|
|
|
00000080 0b 52 c2 92 86 fe 57 0d da fe 62 44 89 ce 65 4f |.R....W...bD..eO|
|
|
|
|
|
00000090 a5 8d 29 8e 10 50 |..)..P|
|
2013-12-20 16:37:05 +00:00
|
|
|
>>> Flow 4 (server to client)
|
|
|
|
|
00000000 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 00 |..........@.....|
|
crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +00:00
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00000010 00 00 00 00 00 00 00 00 00 00 00 29 56 67 0c 28 |...........)Vg.(|
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00000020 ca 74 e1 ae c6 e2 30 3b f2 8b f0 fd c2 eb 11 c0 |.t....0;........|
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00000030 0e 50 eb d8 4e de e3 32 6b 69 77 d8 d7 bd 94 30 |.P..N..2kiw....0|
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00000040 1e bf 03 f0 31 98 d8 07 c0 27 4b 17 03 03 00 40 |....1....'K....@|
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2013-12-20 16:37:05 +00:00
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00000050 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
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crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +00:00
|
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00000060 97 7f df af a3 9e cc a1 64 5f ab 91 8a 6f fd 19 |........d_...o..|
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00000070 be 94 95 6d bb de 12 a9 54 10 b5 95 f3 68 77 73 |...m....T....hws|
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00000080 14 09 b7 3b ca b8 88 6d fd 0a 2d 24 c1 94 ce ce |...;...m..-$....|
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2013-12-20 16:37:05 +00:00
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00000090 15 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........|
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crypto/ecdsa: make Sign safe with broken entropy sources
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>
2015-01-27 07:00:21 +00:00
|
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000000a0 00 00 00 00 00 04 6d b7 9e 15 51 c7 f8 de ab d0 |......m...Q.....|
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000000b0 a0 45 7f 4f bc 59 73 45 e9 a8 b1 0e 9b c3 36 c7 |.E.O.YsE......6.|
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000000c0 cb db 55 19 db |..U..|
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