Research On Keccak-like Hash Function

Hash function is one kind of important cryptographic algorithms, and mainly used for dataintegrity detection, digital signature and generating random numbers, etc. In October2012,National Institute of Standards and Technology elected Keccak as the new hash functionstandard. This paper studies cryptographic properties of Keccak-like hash function, and hasmainly carried on the following four aspects:1. According to the transformation rules of in Keccak, this paper presents n-gramKeccak-like nonlinear transformation model. We deals with the transformation rules of n-gramKeccak-like nonlinear transformation model, proves that the necessary and sufficient conditionfor this model is bijective when n is odd, presents the permutation properties of this model. Thispaper studies the differential properties of n-gram Keccak-like nonlinear transformation model,proves that differential probability is invariant about cyclic shift of differential pair, provides therange of differential probability, presents the structure and count of nontrivial maximum andminimum differential probability. This paper gives the method calculating the differentialprobability of n-gram Keccak-like nonlinear transformation model with differential pair known,and the computational complexity isO (n4) O(2n). Researching on the linear correlation, thispaper proves that collelation coefficient is invariant about cyclic shift of linear approximation,gives the value rage of collelation coefficient, gives the structure of linear approximation whencollelation coefficient is12and12.2. According to the main linear transformation in Keccak, this paper presentsKeccak-like linear transformation model based on n m w3-dimensional matrices. By thetransformation rules of Keccak-like linear transformation model, the3-dimensional matrices canbe divided into three different structures, and we get the XOR branch numbers of differentstructures. In the paper, we provide the theorems and algorithms for solving the inversetransformation.3. This paper deals with differential properties of compression function in Keccak, gives therelation between the differential probability of compression function and in Keccak,provides the second largest differential probability and its structure, and gives the range ofdifferential probability. In the paper, we proves that the differential probability of compressionfunction is invariant about cyclic shift of differential pair on z-axis(the length is w),so if we getone differential characteristics with differential high-probability we can get w differentialcharacteristics with the same differential probability. For differential pair known, we give the method that fast computing differential probability of compression function in Keccak.4. This paper studies differential cryptanalysis of reduced-round Keccak. We study thedifferential characteristics of reduced-round Keccak, give the sufficient condition and algorithmsearching for high-probability differential characteristics. Taking Keccak-f [1600]as an example,we provide the specific procedure and result. In this paper, we point out the differentialcharacteristics error in two documents, analyze the causes, and illustrate the superiority of ourconclusion by comparing with other results.