I have a safe prime generator I'd like to speed up. I can benefit from a significant performance gain if the high order bit in the returned prime can be either 1 or 0. The returned prime would be randomly either 2048- or 2047-bit.
Would this be a problem? Is the possibility of a 2047-bit prime less secure enough to be concerned about?
This is not for RSA; I will not be multiplying the prime with another. It's more along the lines of Diffie-Hellman.