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modsqrt: return success if taking square root of 0.

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My test for whether x has a square root was based on testing whether a
large power of x was congruent to 1 mod p, which is a fine test
provided x is in the multiplicative group of p, but would give a false
negative on the one possible input value that _isn't_ - namely zero.

The actual number returned from the function is fine (because that too
is a large power of the input, and when the input is 0 that's
foolproof). So I just needed to add a special case for the returned
'success' flag.
This commit is contained in:
Simon Tatham 2019-01-03 13:10:26 +00:00
parent 0d9ab2f14b
commit 34d78286e6
1 changed files with 4 additions and 1 deletions
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mpint.c
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@ -2286,7 +2286,10 @@ mp_int *monty_modsqrt(ModsqrtContext *sc, mp_int *x, unsigned *success)
unsigned eq1 = mp_cmp_eq(&tmp, monty_identity(sc->mc));
if (i == 0) {
*success = eq1;
/* One special case: if x=0, then no power of x will ever
* equal 1, but we should still report success on the
* grounds that 0 does have a square root mod p. */
*success = eq1 | mp_eq_integer(x, 0);
} else {
monty_mul_into(sc->mc, &tmp, toret, &power_of_zk);
mp_select_into(toret, &tmp, toret, eq1);