Security Analysis And Design Of The Hash Functions

Hash function is one of the most important embranchment in modern cryptology, which is widely used in digital signature schemes, message authentication and integrity checking. Recently, many break through have been made in Hash function's cryptanalysis. Now, designing, analysing and evaluating a Hash function have become a hot topic in cryptology field.Design of hash functions includes iterated structure design and compression function design. Basic design principles and common attack methods are reviewed in this paper, the most classical iterated structure, Merkle-Damgard structure is described, limitations and leaks are also studied. On this basis, the paper explores three kinds of forms of compress functions of classic Hash, discusses the relationship between addition arithmetic and XOR arithmetic. Main work as follows:Chabaud-Joux attack, which is based on finding a corrective pattern for the register is one of the most successful attacks on the SHA algorithms. In this paper, we present three kinds of variant forms of compress functions of SHA-256, and analysis the security of three variants against the Chabaud-Joux attack compared with SHA-256. It follows that the selection of the compression function's structure highly affects the complexity of the attack. Furthermore, a local collision in the vulnerable variant is presented.SMASH is a new hash function proposal, based on the property of forward prediction. The design principle and attack method of SMASH are described, and some approaches such that SMASH can resist on this attack are suggested. The main measures are destroying forward prediction property and increasing the complexity of find divinable difference.Addition arithmetic and XOR arithmetic are usually used in the design of hash functions; the corresponding differences are called addition difference and XOR difference, respectively. The paper presents a sufficient and necessary condition of the transition of addition-XOR differences, and an algorithm of finding the integer pairs which preserve addition differences when XOR differences are given, and studies their applications in analyzing the security of Hash function. As an example, we show how to find a pseudo-collision in a Message Authentication Code function which is called ASP.