Randomness Analyses of the Secure Hash Algorithms, SHA-1, SHA-2 and Modified SHA

This paper introduces a security analysis scheme for the most famous secure hash algorithms SHA-1 and SHA-2. Both algorithms follow Merkle Damgård structure to compute the corresponding hash function. The randomness of the output hash reflects the strength and security of the generated hash. Therefore, the randomness of the internal rounds of the SHA-1 and SHA-2 hash functions is analyzed using Bayesian and odd ratio tests. Moreover, a proper replacement for both algorithms is proposed, which produces a hash output with more randomness level. The experiments were conducted using a high performance computing testbed and CUDA parallel computing platform.