International Association
for Cryptologic Research

SQIsign is an isogeny-based, post-quantum signature scheme over supersingular elliptic curves that represents isogenies via objects of a quaternion algebra, enabling very compact signatures and efficient computations. However, the SQIsign implementation relies on GMP library, which dynamically allocates size of integers so hinders portability and complicates memory control. Furthermore, a consolidated worst-case bound on the integer coefficients representing quaternion algebra elements does not exist, leaving the required static precision unclear for a GMP-free implementation.

In this work, we audit every routine in the SQIsign Round-2 specification that manipulates quaternion elements and prove a uniform worst-case bound on coefficient growth. Complementing the theoretical bounds, we repeat the key generation and signing process of Round-2 SQIsign reference code implemented with GMP library, record peak operand sizes, and derive experimental bounds. Based on this bound, we choose a fixed-size precision representation and implement SQIsign in C without dynamic allocation such as GMP library.