New Synthesis Tool Extends Small-Scale Quadratic Function Design to 9 Bits

Global: New Synthesis Tool Extends Small-Scale Quadratic Function Design to 9 Bits

A team of researchers has introduced a software tool that can generate minimal Boolean circuits for quadratic functions up to nine input bits while keeping the AND‑gate depth to one. The tool, released alongside an IEEE article and hosted on CodeOcean and GitHub, aims to reduce the computational effort required for circuit synthesis in cryptographic contexts.

Background

The task of finding the smallest circuit that implements a specific Boolean function is a classic problem in electronics and is known to be NP‑hard. Traditional synthesis tools, often called synthesizers, target large‑scale designs such as entire chips, whereas cryptographic applications frequently involve much smaller functions.

Existing Solutions

Prior approaches for small‑function synthesis include depth‑first search methods introduced by Ullrich in 2011, SAT‑solver based tools such as the one described by Stoffelen in 2016, and specialized techniques that exploit subfield decomposition. These methods typically handle functions of five bits or fewer, and occasionally six bits for quadratic cases, because the required computation time grows rapidly with input size.

New Synthesis Tool

The newly released tool expands the feasible input size to nine bits for quadratic functions. It focuses on minimizing the number of AND gates while maintaining an AND‑depth of one, a metric that directly influences side‑channel resistance and implementation efficiency.

Technical Highlights

According to the authors, the algorithm combines exhaustive search with heuristic pruning to explore the design space more efficiently than earlier methods. By constraining the circuit to a single layer of AND gates, the tool simplifies the optimization problem without sacrificing the ability to generate compact implementations.

Performance and Scope

Benchmark results reported in the accompanying paper indicate that the tool requires less processing time than existing alternatives for comparable problem sizes. This efficiency enables researchers to explore circuit designs for functions up to nine bits, surpassing the six‑bit limit that has constrained earlier studies.

Availability and Impact

The source code is publicly available on GitHub (https://github.com/seduval/implem-quad-sbox) and has been packaged for reproducibility on the CodeOcean platform. By providing a more time‑effective synthesis method, the tool may facilitate further research into side‑channel‑protected implementations and other cryptographic primitives that rely on small, well‑optimized Boolean functions.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.