A Method of Generating 8 × 8 Substitution Boxes Based on Elliptic Curves

An Injective S-Box Design Scheme over an Ordered Isomorphic Elliptic Curve and Its Characterization

“…It is clear from the table that the LAP of the proposed S-boxes is low, while their NL and AC are high enough to resist the linear attacks efficiently. Note that the average value of LAP of the proposed S-boxes is 0.1445 which is less than that of the S-boxes in [21,22,27,31], while their average NL and AC are 106 and 254 which are higher than that of [20,26,27,29,[31][32][33] and [28,30,31], respectively. This implies that the proposed method is capable of generating S-boxes with high security against linear attacks than some of the listed S-boxes.…”

“…We generated the S-boxes Tables 2-4, respectively. A comparison of the experimental results with the strongest S-boxes generated by the algorithms in [20][21][22][26][27][28][29][30][31][32][33][34] is also conducted in this section.…”

“…Thus, by choosing some large prime, the proposed method can generate a large number of dynamic S-boxes, and therefore it can easily resist the brute force attacks. For the comparison, the maximum possible number of S-boxes that can be generated by the other schemes [20][21][22] over an EC is also listed in Table 6. It is evident from Table 6 that the proposed method is more suitable for the generation of dynamic S-boxes than the listed schemes.…”

“…Jung et al [19] characterized Sboxes over hyperelliptic curves. Hayat et al [20,21] proposed different methods for the generation of an 8 × 8 S-box by using an elliptic curve (EC) over a prime field. Actually, the scheme in [21] is a generalization of the scheme in [20].…”

“…Hayat et al [20,21] proposed different methods for the generation of an 8 × 8 S-box by using an elliptic curve (EC) over a prime field. Actually, the scheme in [21] is a generalization of the scheme in [20]. These techniques use -coordinates of the points on the EC followed by modulo 256 operation.…”