I have N of 1024 bits. I need to convert a message M ( 512 bits ) into Montgomery reduction form as below.
M' = M * R^{-1} mod N
where , R = 2 ^ 512 (mod N)
How can I achieve the result ?
Montgomery Reduction form using OpenSSL library
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The following should work if you use the bignum package from OpenSSL directly.
Use the function
BN_mod_expto calculate your R=2^512 (mod N).Afterwards you calculate the multiplicative modulo inverse of R by calling
BN_mod_inverse. This will give you the R^-1.Once done you just calculate your M' by calling
BN_mod_multo do the multiplication using your just calculated R^-1 and your original message.You'll find the functions mentioned above in the OpenSSL BigNum Package. They are located in the include file: openssl/bn.h