Abstract
Due to the success of differential and linear attacks on a large number of encryption algorithms, it is important to investigate relationships among various cryptographic, including differential and linear, characteristics of an S-box (substitution box). After discussing a precise relationship among three tables, namely the difference, auto-correlation and correlation immunity distribution tables, of an S-box, we develop a number of results on various properties of S-boxes. More specifically, we show (1) close connections among three indicators of S-boxes, (2) a tight lower bound on the sum of elements in the leftmost column of its differential distribution table, (3) a non-trivial and tight lower bound on the differential uniformity of an S-box, and (4) two upper bounds on the nonlinearity of S-boxes (one for a general, not necessarily regular, S-box and the other for a regular S-box).
| Original language | English |
|---|---|
| Pages (from-to) | 45-63 |
| Number of pages | 19 |
| Journal | Designs, Codes and Cryptography |
| Volume | 19 |
| Issue number | 1 |
| Publication status | Published - Jan 2000 |
Keywords
- Boolean Functions
- Cryptography
- Differential attack
- Linear attack
- Nonlinearity
- S-boxes