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51 lines
1.7 KiB
51 lines
1.7 KiB
--- lib/Crypto/PublicKey/ElGamal.py
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+++ lib/Crypto/PublicKey/ElGamal.py
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@@ -153,33 +153,33 @@ def generate(bits, randfunc, progress_fu
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if number.isPrime(obj.p, randfunc=randfunc):
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break
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# Generate generator g
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- # See Algorithm 4.80 in Handbook of Applied Cryptography
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- # Note that the order of the group is n=p-1=2q, where q is prime
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if progress_func:
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progress_func('g\n')
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while 1:
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+ # Choose a square residue; it will generate a cyclic group of order q.
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+ obj.g = pow(number.getRandomRange(2, obj.p, randfunc), 2, obj.p)
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+
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# We must avoid g=2 because of Bleichenbacher's attack described
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# in "Generating ElGamal signatures without knowning the secret key",
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# 1996
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- #
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- obj.g = number.getRandomRange(3, obj.p, randfunc)
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- safe = 1
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- if pow(obj.g, 2, obj.p)==1:
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- safe=0
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- if safe and pow(obj.g, q, obj.p)==1:
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- safe=0
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+ if obj.g in (1, 2):
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+ continue
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+
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# Discard g if it divides p-1 because of the attack described
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# in Note 11.67 (iii) in HAC
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- if safe and divmod(obj.p-1, obj.g)[1]==0:
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- safe=0
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+ if (obj.p - 1) % obj.g == 0:
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+ continue
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+
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# g^{-1} must not divide p-1 because of Khadir's attack
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# described in "Conditions of the generator for forging ElGamal
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# signature", 2011
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ginv = number.inverse(obj.g, obj.p)
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- if safe and divmod(obj.p-1, ginv)[1]==0:
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- safe=0
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- if safe:
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- break
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+ if (obj.p - 1) % ginv == 0:
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+ continue
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+
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+ # Found
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+ break
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+
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# Generate private key x
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if progress_func:
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progress_func('x\n')
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