Optimal S box construction method and circuit

Abstract

The invention discloses an optimal S box construction method and an optimal S box construction circuit, which belong to the technical field of communication. The method comprises the following steps of: 1) setting x0x1x2x3 to be the input information of an S box, performing a logical AND operation on x0 and x1, and updating x2 by using a value obtained by performing an XOR operation on a logical AND operation result and x2; 2) performing a logical OR operation on x1 and the updated x2, and updating x3 by using the value obtained by performing the XOR operation on a logical OR operation result and x3; 3) performing the logical AND operation on the updated x2 and the updated x3, and updating x0 by using the value obtained by performing the XOR operation on the logical AND operation result and x0; 4), performing the logical OR operation on the updated x0 and the updated x3, and updating x1 by using the value obtained by the logical OR operation result and x1; and 5) adopting the x0x1x2x3 updated by the steps 2) to 4) as the output of the input information x0x1x2x3 set by the step 1) and passing through the S box. The circuit comprises four XOR operation units A1, A2, A3 and A4, two logical AND operation units B1 and B2 and two logical OR operation units C1 and C2. By the method and the circuit, a great number of optimal 4*4 S boxes can be generated rapidly, and hardware realization cost is low.

Description

technical field [0001] The invention proposes an optimal S-box construction method and its circuit, which can be applied to quickly generate a large number of 4×4S-boxes with optimal cryptographic properties, and the hardware implementation cost of this type of S-box is very small, which belongs to the field of communication technology . Background technique [0002] S-box is a multi-output Boolean function, which is an extremely important non-linear component in the construction of cryptographic algorithms, and is widely used in various cryptographic schemes. In particular, almost all lightweight cryptographic algorithms designed for practical application requirements such as resource-constrained environments use 4×4 S-boxes. Since lightweight cryptographic algorithms are usually implemented by hardware, the hardware implementation cost and security of the S-box as the basic module of the algorithm are equally important. The present invention proposes an efficient method ...

AI Technical Summary

Problems solved by technology

[0011] (2) Differential uniformity

Considering that the permutation P defined on the set {0,1,K,15} has a total of 16!≈2 44.25 Only a few of them satisfy the conditions of Step2 and Step3 at the same time, so constructing the optimal S-box by random selection, especially when a large number of S-boxes need to be selected, will be a very time-consuming task

In addition, because the optimal S-boxes constructed are randomly generated, it is usually impossible to write simple mathematical formulas for such S-boxes, so the algebraic degree and number of terms of the Boolean function expressions are large, which makes the hardware implementation The number of combined logic gates required is large, which will increase the overall hardware implementation cost of the cryptographic algorithm

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