The Partial Demonstration Of Tu-Deng Conjecture And Integral Attack Of PRESENT Algorithm

Tu-Deng conjecture has played a significantly important role in the research of alge-braic immunity. Based on the conjecture, people have constructed the boolean functionswith the optimal algebraic immunity and high nonlinearity. First, this paper studys thevalidity of Tu-Deng conjecture. In view of the verified result, we have proved Tu-Dengconjecture in the cases when k is random and t is less-than-or-equal-to219, which makebetter results than the previous. The other work of this paper is to discuss the securitycryptanalysis of PRESENT by analysing the algebraic degree of S-box and the propertyof the diffusion based on the bit pattern integral attack. The main outcome is putting for-ward the the analytical method of multiplication on bit pattern and showing the6roundintegral distinguisher of PRESENT algorithm which achieve the9round integral attackof PRESENT with the293.1time complexity,220.4data complexity and277bytes spacecomplexity respectively.