Efficient multiplications in finite fields for multivariate signatures

There has been a continuous and increasing interest in research and application of Wireless Sensor Networks (WSNs). Although the future of WSNs is very prospective, the security issues become more and more important because they are used for very critical applications in engineering areas. Furthermore, they are very vulnerable and thus attractive to attacks because of human-unattended deployment and their limited prices. Generally, they are protected by public key cryptosystems. Such systems depends on the difficulty of the elliptic curve discrete logarithms or integer factorizations. However, they can be attacked by Shor’s algorithm on quantum computers. Multivariate Public Key Cryptography (MPKC) schemes are secure to attacks by quantum computers. Among such schemes, multivariate signatures use various multiplications in a finite field, which are time-consuming operations during signature generations. Thus, we focus on improving multiplications in finite fields for multivariate signatures. We propose a variant of Mastrovito multiplications based on trinomial, Special Trinomial (ST), pentanomial, Special Pentanomial (SP), Equally-spaced-polynomial (ESP), All-One-polynomial (AOP), and successive-one-polynomial (SOP). Our design is implemented on hardware and can be used to improve the implementations of multivariate signatures including UOV, enTTS and Rainbow for protecting data security in WSNs.