Study On Character Of (x+k)mod2~n And Application In Database Encryption System

Added K on modulo 2ⁿ operation - Y=(X+K)mod2ⁿ is a code link which is often used in cipher algorithms , here K is a fixed constant. The link has a good non-linear character which is widely used in block cipher, stream cipher and hash function. In this paper, there are three ways to study cipher character of (X+K)mod2ⁿ . The differential and linear character of ( X + K)mod 2ⁿ, the equivalent degree between ( X + K)mod 2ⁿ and X⊕K is studied, the problem of Solving Differential Equations of ( X + K)mod 2ⁿ. Based on the harvest, a guess and determine attack on a stream cipher--SNOW1.0 and a truncated differential attack on a block cipher algorithm--CFFC are improved, The improved results are better than the original results. The main works and creations are as the following:1. The differential and linear character of ( X + K)mod 2ⁿ is studied.The characters of structure, counting lower bound of the input difference, the output difference, constant ((?)X , (?)Y , K)is given, when the differential probability is to be the minimum value 0. The maximum value of the differential probability is given, when the constant K is random given. A O(n) algorithm to compute the linear approximation of (X+K)mod 2ⁿ is given. It can help us get the formula to solve probality ofα·X⊕β·( X + K mod 2ⁿ)⊕γ·K= 0 on the condition of the combination (α,β,γ) are random given.2. The equivalent degree between ( X + K)mod 2ⁿ and X⊕K is studied.Based on the"big probability of selecting the priority principle"of the exhaustive attack, a best algorithm is given to solve the equivalence problem between ( X + K)mod 2ⁿ and X⊕K on the condition of the K is the special value, and this algorithm is used in guess and determine attack on SNOW1.0 . Hawkes and Rose's method about guess and determine attack on SNOW1.0 is improved, the data complexity has decreased from 2⁹⁵ to 2⁹⁰, while the process complexity is remained basically.3. The problem of Solving Differential Equations of ( X + K)mod 2ⁿ is studied.The O(n) polynomial time algorithms are given to solve the Differential Equations (X + K)mod 2 n⊕β= ((X⊕α) + K)mod 2ⁿ on the condition of the input X(or the output Y) is known, hereα,βmeans the input difference and the output difference. An example of truncated differential attack on a block cipher algorithm-CFFC is furnished, and the results of the truncated differential attack on CFFC is improved by this algorithm, the process complexity has decreased from 2⁴⁷ to 2¹⁸.4.Designed a block cipher algorithm-ICFFC algorithm,designed a database cryptosystem based on this algorithm.Designed a design a block cipher algorithm-ICFFC algorithm used and sbox, showed that ICFFC can resist differential attack, linear attack and truncated differential attack, designed a database cryptosystem based on -ICFFC algorithm.