Abstract
In this paper, a platform named PEIGEN is presented to evaluate security, find efficient software/hardware implementations, and generate cryptographic S-boxes. Continuously developed for decades, S-boxes are constantly evolving in terms of the design criteria for both security requirements and software/hardware performances. PEIGEN is aimed to be a platform covering a comprehensive check-list of design criteria of S-boxes appearing in the literature. To do so, the security requirements are first intensively surveyed, existing tools of S-boxes are then comprehensively compared, and finally our platform PEIGEN is presented. The survey part is aimed to be a systematic reference for the theoretical study of S-boxes. The platform is aimed to be an assistant tool for the experimental study and practical use of S-boxes. PEIGEN not only integrates most of the features in existing tools, but also equips with functionalities to evaluate new security-related properties, improves the efficiency of the search algorithms for optimized implementations in several aspects. With the help of this powerful platform, many interesting observations are made in-between the security notations, as well as on the S-boxes used in the existing symmetrickey cryptographic primitives. PEIGEN will become an open platform and welcomes contributions from all parties to help the community to facilitate the research and use of S-boxes.
Highlights
The substitution-box, or S-box for short, is commonly used in the design of symmetric cryptography primitives to offer non-linearity
Given a set of n-bit S-boxes and the specific implementation configuration, Peigen can provide their implementations under various techniques, which are good with respect to different merits: 1. Bitslice gate complexity (BGC), Gate equivalent complexity (GEC), and Multiplicative complexity (MC): outputs implementations optimized for area and code size, i.e., with minimized number of gates/equivalent gates under different implementation techniques, or with minimized number of non-linear operations; 2
For readers who are interested in the resulting summary on cryptographic properties of existing S-boxes, details are provided in the supplementary materials, which provide concisely summarized and thoroughly detailed evaluations
Summary
The substitution-box, or S-box for short, is commonly used in the design of symmetric cryptography primitives to offer non-linearity. To make a better trade-off between the security and performance, there is a line of research developing tools for finding the optimal implementations. In the later part of this paper, we follow the line of research in developing tools for evaluating and implementing S-box. Security and implementation aspects are hard to consider simultaneously This motivates us to present a platform named Peigen for evaluating the security properties, finding optimal implementations for given S-boxes, and generating all suitable S-boxes when the security and performance requirements are given. When finding implementations and generating new n-bit S-boxes, it is more efficient than existing tools for n = 3, 4 It only supports 3 ≤ n ≤ 8-bit S-boxes, which is mainly because of the application of specific optimization tricks, it can be extended to support larger n.
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