# Re: Exponent 3 damage spreads...

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Jostein Tveit wrote:

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```Ben Laurie <[EMAIL PROTECTED]> writes:

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```...thought this might interest people here.
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Anyone got a test key with a real and a forged signature to test
other implementations than OpenSSL?

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If I understand the attack mathematics correctly, the following algorithm should give you an alleged signature value that would be mistakenly accepted by a flawed RSA implementation. I didn't implement the algorithm, and I will not make suggestions as a convenient big number arithmetic tool to implement it.
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Note: The algorithm output value is NOT A FORGED SIGNATURE, since a non-flawed RSA signature verification implementation will correctly reject it. Nonetheless, using public exponent 3 with any use of RSA should be deprecated.
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For the record, I am referring to
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Hal Finney, "Bleichenbacher's RSA signature forgery based on implementation error" Wed, 30 Aug 2006
```http://www.mail-archive.com/cryptography@metzdowd.com/msg06537.html

Input:

N, large public modulus (of unknown factorization)
h, hash value

Constant:

p: hex 01 FF 00 30 21 30 09 06 05 2B 0E 03 02 1A 05 00 04 14

A random binary source (e.g. large enough PRNG output)

Algorithm:

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(A) find the largest value of r such that b=(p*2^20+h)*2^(8r) such that b+2^(8r)-1<N
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(B) select random a, 0<a<N^2, then set c=a*N^2+b+2^(8r)-1

(C) using a simple binary search, find the d = integer cubic root of c

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(D) if d^3<a*N^2+b, go back to step (B) -- if it occurs with a high probability, that's a failure of the approach proposed here, intuition suggests that the probability is either very close to zero, or very close to one
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(E) set alleged signature s=d mod N (indeed, d<N, so s=d) and validate (merely as a software self-check) that (s^3 mod N) div 2^(8r) equals (p*2^20+h)
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(F) output alleged signature s

Regards,

--

- Thierry Moreau

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