The Analysis Of Differential Probability Based On Arithmetic Operation In Block Cipher

In the design of block cipher algorithm, the designers hope to meet the specified safety design requirements by increasing the differential confusion and diffusion. So far, the key component of the popular cryptographic algorithm, such as RC5, RC6[19], Threefish, SHA-X[13], not only use the box but also use arithmetic operations in the round function to increase the safety of the algorithm. Now the basic operation commonly used are modular additions, bitwise XORs and interword rotations, which are functionally complete. And in the process of the operations, increasing the use of the basic arithmetic operations can increase the safety of the cipher algorithm on the basic of the efficient software and hardware implementation. So in the design of block cipher algorithm, to increase the operations such as modular additions, bitwise XORs and interword rotations is a commonly constructed method. Our paper adds subtraction operation based on modular additions and bitwise XORs. By studying the existed differential probability calculation method[24]; calculate other differential probability structures of increasing subtraction operation by the differential probability calculation method. This paper does the analysis consisted of five chapters on difference corresponding probability under the basic operation, gets the main conclusions:1. Introducing the corresponding probability xdp+calculation method of existing operational structure of the difference, this paper uses the carry state function and the calculation method of the carry bits, represents the edges which connected relationships in the graph theory in the process of the operations, constructs the edges’adjacency matrix, According to matrix multiplication, the probability of the differential corresponding can be calculated. Meanwhile, the calculation process of the differential probability of adp(?) can be verified.2. In order to calculate the differential corresponding’ probability,we use the operation units consisted of modular additions subtraction operations and bitwise XORs. In the paper, we reconstruct two combinations of group operations. According to calculation method of S-function, we deduce the new structures’probability calculation formulas of the difference corresponding. The keys of the new structures’probability calculation formulas are the carry state function, the carry results of bitwise operations, the edges’ adjacency matrix, and than matrix multiplication. In order to verify the correctness of the calculation formulas, we iterate through all the results using computer programs, the result confirms the formulas’ effectiveness.3. Compared the differential probability under four different operations structures, we have that the same difference corresponding’ probabilities are not the same under different operations; and the different differences corresponding’ probabilities are not the same under same operations. It shows that a variety of operations can be used on the design, design approach can be flexible chosen.4. This paper summarizes the differential probability based on the three kinds of the combination: addition, subtraction and xor, which can provide more analytical tools for cryptogram analysts.