Cryptanalysis of Cryptmt: Effect of Huge Prime Period and Multiplicative Filter

CryptMT (Cryptographic Mersenne Twister) is an 8-bit pseudorandom integer generator for a stream cipher. It combines an F2-linear generator of period 219937 − 1 and a multiplicative filter with 32-bit memory. We analyze its security against some standard cryptanalytic attacks for filter generators. It is proved that CryptMT has strong resistance against them: CryptMT has a period of 219937 − 1, the correlations among the consecutive 624-bytes of outputs are of order 2−19937, the algebraic degree of the output bits with respect to the bits in Key and IV is expected to near to the size of Key and IV. The Key size and IV size are variable, up to 2048-bit for each. We claim that CryptMT has the same security level with the minimum of the key size and the IV size. CryptMT is 1.5–2.0 times faster than the optimized AES CTR mode with 256-bit security level.