A New Standard SHA - 3 Analysis Of Hash Function

The importance of information security is becoming more and more prominent.Cryptology, as the basic and core technique of information security, is gaining broadattention. Hash function is an important branch of cryptology, and it is widely used invarious security applications and network protocols. Some hash algorithms, such asMD5and SHA-1, was proved to be vulnerable. Thus, National Institute of Standardsand Technology (NIST) launched a worldwide public competition aiming at theselection of a new standard for hash function in2007. Keccak is one of the64candidates submitted to the competition. On October2nd2012, NIST announced itsselection of Keccak as the new hash standard. Differ from the well-knownMerkle-Damgard structure, Keccak adopt a new design concept of the so-calledsponge construction. Keccak possess many excellent properties such as goodcompatibility and low implementation cost. Keccak has been becoming a researchhotspot since it was first presented, especially after it was announced as the winner ofthe competition. Our works are summarized as follows:First, we carried out a detailed study of the five mappings θ, ρ, π, χ and ι inSHA-3permutation. We got the inverse mappings of the five mappings and thusobtained the inverse permutation of Keccak-f. We calculated the input-outputdifferentials of all32cases and constructed the differential distribution table of χ andχ-1by mathematical deduction.Second, we proposed a new search algorithm of Double Kernel form differentials.Our new algorithm has a great advantage in computing complexity compared withexisting algorithms. By using our new algorithm, we obtained all256Double Kernelform differentials. We also proved that Double Kernel form differentials withhamming weight4and below do not exist.Last, we made a security analysis of SHA-3in light of statistical performance,symmetrical property of Keccak-f and security of the inverse permutation of Keccak-f.Our results show that Keccak has a good statistical performance, internal differentialcryptanalysis using the symmetrical property of Keccak-f can only be applied to avery limited number of rounds and, the existence of inverse permutation of Keccak-fwould not pose a substantial threat to the security of Keccak.