The substitution box (S-box) is one of the major components of cryptographic algorithms. An important issue for cryptographic algorithm designers in ensuring sufficient security from linear cryptanalysis, one of the most powerful attacks, is finding an S-box with a sufficiently low linear spectrum. However, to the best of our knowledge, most of the published S-box analysis tools cannot generate linear approximation tables for large S-boxes, such as 16-bit S-boxes. Even tools that support the generation of 16-bit linear approximation tables using parallel processing, such as Eval16BitSbox, require a long time. We used bitslice, which can efficiently process bitwise operations in parallel by taking advantage of independent operations, for generating a linear approximation table. In this study, the linear approximation table generation method implemented using the element unit operation of the existing S-box was upgraded to a vector unit operation in a bitslice manner. This improved method enabled the immediate creation of tables, even for 16-bit Sboxes. This approach allows cryptographic algorithm designers to consider a wider variety of S-boxes.
INDEX TERMS Large size S-box, Bitsliced implementation, Linear approximation Table21each round. When using an S-box for a nonlinear function, 22 this attack uses a difference distribution table (DDT) of the S-23 box. The DDT is a chart of how often a difference in the input 24 bit makes a difference in the output bit. Linear cryptanalysis 25 uses an equation generated by a linear approximation of 26 the relationship between the input and output bits of the S-27 box. Such an approximation can be achieved using a linear 28 approximation table (LAT) of the S-box. 29 Cryptanalysis largely utilizes these two tables. Finding an 30 S-box for which both properties are secure is therefore an 31 important issue for cryptographic algorithm designers. S-32 box analysis tools, such as PEIGEN, SAGE, SET, BSAT, 33 etc., generally provide facilities for the generation of DDT 34 and LAT [12]-[15]. However, as the bit size of the S-box 35 grows to around 16 bits, most tools do not support LAT 36 generation, or the generation process is not finished. In the 37 most widely used table generation method for an n-bit S-box, 38 2 2n computations are required to generate the DDT, and 2 3n 39 computations are required to generate the LAT. Hence, for