Hi
While dealing on RSAKeyGen I accidentally discovered a set of numbers for
which BN_mod_exp is giving a wrong result. I want to know whether I am wrong
or even if my code is right, is there some limitation to BN_mod_exp?
I am interested to calculate (x^y)mod z by using BN_mod_exp(r,x,y,z) where
the result is stored in r. I used openssl-0.9.6 downloaded from the openssl
site two days back.
I will give here the values of x,y,z and r in hex. Could anybody please
throw some light on the seemingly wrong result?
x = 3
y = 2DC6C0
z =
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
r =
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
And when I used a large integer calculator and gmp library as well, I found
that both gmp and the calculator were giving the same reult but of course
different from ssl .ssl's output is in the varaible r ,given above.
gmp and the calculator gave the below number:
0176B344F2A78C0000
Now,I went to the ssl BIGNUM code and found that for odd modulus, it
executes montogomery and for even it uses BN_mod_exp_simple. If you use
simple for all cases it gives slow but correct result but montogomery seems
to fail in case of some odd modulus like in the present case.
Any idea please?
bye
Thanks
Biswa
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