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Date: Mon, 19 Oct 2015 17:01:37 -0200 From: Marcos Simplicio <mjunior@...c.usp.br> To: discussions@...sword-hashing.net Subject: Re: [PHC] Re: BlaMka loses entropy Hi, Bill. I was about to point out the mistake with a Java snippet we developed to check if BlaMka is a permutation for several bit-lengths. You were faster than me, though :) BR, Marcos Simplicio. On 19-Oct-15 16:39, Bill Cox wrote: > D'oh! I was wrong. The BlaMka round preserves entropy. Sorry about the > mistake. I've been doing mod p arithmetic so much I forgot this is mod > 2^64, not mod p. > > Bill > > On Mon, Oct 19, 2015 at 11:17 AM, Bill Cox <waywardgeek@...il.com> wrote: > >> This concerns me a great deal. The Blake2 reduced round G is invertible. >> This proves there is zero entropy loss up to the point that we do the >> compression. The BlaMka round does lose entropy. >> >> Basically, the regular Blake2 addition step looks like: >> >> a = (a + b) % p >> >> After executing it, we know a+b, and b, and can invert it by subtracting b >> from a+b. The BlaMka multiplication step replaces the addition step, and >> looks like: >> >> a = (a + b + 2*(a % 2^32)*(b % 2^32)) % p >> >> The idea was to use something like a latin square defined by a + b + 2*ab, >> but that's now what we have here. The following _is_ invertible: >> >> a = (a + b + 2*a*b) % p >> >> By using only the low order words of a and b, we lost information. Here's >> a simple Python script to prove it: >> >> def BlaMka(a, b, p, mask): >> return (a + b + 2*((a*b) & mask)) % p >> >> def printSquare(p, mask): >> for a in range(p): >> for b in range(p): >> print "%2d" % BlaMka(a, b, p, mask), >> print >> >> p = 13 >> mask = 3 >> printSquare(p, mask) >> >> When run, it produces: >> >> 0 1 2 3 4 5 6 7 8 9 10 11 12 >> 1 4 7 10 5 8 11 1 9 12 2 5 0 >> 2 7 4 9 6 11 8 0 10 2 12 4 1 >> 3 10 9 8 7 1 0 12 11 5 4 3 2 >> 4 5 6 7 8 9 10 11 12 0 1 2 3 >> 5 8 11 1 9 12 2 5 0 3 6 9 4 >> 6 11 8 0 10 2 12 4 1 6 3 8 5 >> 7 1 0 12 11 5 4 3 2 9 8 7 6 >> 8 9 10 11 12 0 1 2 3 4 5 6 7 >> 9 12 2 5 0 3 6 9 4 7 10 0 8 >> 10 2 12 4 1 6 3 8 5 10 7 12 9 >> 11 5 4 3 2 9 8 7 6 0 12 11 10 >> 12 0 1 2 3 4 5 6 7 8 9 10 11 >> >> Note that 1 and 5 appear twice in the second column, while 3 and 6 are >> missing. This 4-bit version of BlaMka is clearly not a quasi-group. >> >> My recomendation: switch back to the reduced Blake2b round, and >> incorporate something similar to MAXFORM that runs on the scalar unit. >> This will ensure we do long leak entropy until a compression step. >> Incorporating multiplication into the Blake2 reduced round was a poor >> solution in any case, IMO, since there is 8X parallelism built into the >> Argon2 block hash. The whole point of multiplication chain compute-time >> hardening is to force the attacker to run nearly as long as the defender. >> A free factor of 8X speedup is too high. My top 3 concerns at the moment >> for Argon2 are: >> >> - Entropy loos >> - Too much parallelism >> - Poor compute-time hardening (due to parallelism) >> - Poor in-cache performance (about 3X slower than TwoCats) >> - Somewhat poor GPU resistance. >> >> Using MAXFORM on the scalar unit would solve 4 of my top 5 concerns. The >> poor in-cache performance is not easily fixed, since Argon2's state busts >> out of the SIMD unit registers and lives in L1 cache. For low-memory >> in-cache memory hashing, I plan to replace the Argon2 block hash with most >> likely either the one from TwoCats or preferably Yescrypt if it is fast >> enough. >> >> Bill >> >
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