Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography

Libey Djath (1) , Karim Bigou (1) , Arnaud Tisserand (2)

1 Lab-STICC_UBO_CACS_MOCS
2 Lab-STICC_UBS_CACS_MOCS

Base extension is a critical operation in RNS implementations of asymmetric cryptosystems. In this paper, we propose a new way to perform base extensions using a hierarchical approach for computing the Chinese remainder theorem. For well chosen parameters, it significantly reduces the computational cost and still ensures a high level of internal parallelism. We illustrate the interest of the proposed approach on the cost of typical arithmetic primitives used in asymmetric cryptography. We also demonstrate improvements in FPGA implementations of base extensions on typical elliptic curve cryptography field sizes using high-level synthesis tools.

Keywords: Computer arithmetic; residue number system; modular reduction; hardware implementation

Domains: Computer Arithmetic; Cryptography and Security [cs.CR]; Micro and nanotechnologies/Microelectronics

Libey Djath, Karim Bigou, Arnaud Tisserand. Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography. ARITH: 2019 IEEE 26th Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. ⟨hal-02096353⟩