Imported OpenSSL 1.1.1d
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@@ -30,30 +30,33 @@ int DH_generate_parameters_ex(DH *ret, int prime_len, int generator,
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/*-
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* We generate DH parameters as follows
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* find a prime q which is prime_len/2 bits long.
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* p=(2*q)+1 or (p-1)/2 = q
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* For this case, g is a generator if
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* g^((p-1)/q) mod p != 1 for values of q which are the factors of p-1.
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* Since the factors of p-1 are q and 2, we just need to check
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* g^2 mod p != 1 and g^q mod p != 1.
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* find a prime p which is prime_len bits long,
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* where q=(p-1)/2 is also prime.
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* In the following we assume that g is not 0, 1 or p-1, since it
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* would generate only trivial subgroups.
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* For this case, g is a generator of the order-q subgroup if
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* g^q mod p == 1.
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* Or in terms of the Legendre symbol: (g/p) == 1.
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*
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* Having said all that,
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* there is another special case method for the generators 2, 3 and 5.
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* Using the quadratic reciprocity law it is possible to solve
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* (g/p) == 1 for the special values 2, 3, 5:
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* (2/p) == 1 if p mod 8 == 1 or 7.
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* (3/p) == 1 if p mod 12 == 1 or 11.
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* (5/p) == 1 if p mod 5 == 1 or 4.
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* See for instance: https://en.wikipedia.org/wiki/Legendre_symbol
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*
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* Since all safe primes > 7 must satisfy p mod 12 == 11
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* and all safe primes > 11 must satisfy p mod 5 != 1
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* we can further improve the condition for g = 2, 3 and 5:
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* for 2, p mod 24 == 23
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* for 3, p mod 12 == 11
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* for 5, p mod 60 == 59
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*
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* However for compatibilty with previous versions we use:
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* for 2, p mod 24 == 11
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* for 3, p mod 12 == 5 <<<<< does not work for safe primes.
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* for 5, p mod 10 == 3 or 7
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*
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* Thanks to Phil Karn for the pointers about the
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* special generators and for answering some of my questions.
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*
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* I've implemented the second simple method :-).
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* Since DH should be using a safe prime (both p and q are prime),
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* this generator function can take a very very long time to run.
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*/
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/*
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* Actually there is no reason to insist that 'generator' be a generator.
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* It's just as OK (and in some sense better) to use a generator of the
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* order-q subgroup.
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* for 5, p mod 60 == 23
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*/
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static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
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BN_GENCB *cb)
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@@ -88,13 +91,10 @@ static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
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goto err;
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g = 2;
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} else if (generator == DH_GENERATOR_5) {
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if (!BN_set_word(t1, 10))
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if (!BN_set_word(t1, 60))
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goto err;
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if (!BN_set_word(t2, 3))
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if (!BN_set_word(t2, 23))
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goto err;
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/*
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* BN_set_word(t3,7); just have to miss out on these ones :-(
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*/
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g = 5;
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} else {
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/*
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@@ -102,9 +102,9 @@ static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
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* not: since we are using safe primes, it will generate either an
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* order-q or an order-2q group, which both is OK
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*/
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if (!BN_set_word(t1, 2))
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if (!BN_set_word(t1, 12))
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goto err;
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if (!BN_set_word(t2, 1))
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if (!BN_set_word(t2, 11))
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goto err;
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g = generator;
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}
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