(2026-05) Optimized G+G Signature
2026-05-13
At ASIACRYPT 2023, Devevey, Passelègue and Stehlé proposed the G+G signature, which is designed based on the Fiat-Shamir transform without rejection sampling technique. However, the optimization of the G+G signature have not been studied as extensively as those of Lyubashevsky-type signatures. The contribution of this work is the integration of the Asymmetric Learning with Errors (ALWE) problem into the key generation phase of the G+G signature. We present a more precise estimation method for the largest singular value of the secret key and introduce a new non-spherical Gaussian distribution to characterize the signature distribution. Experimental results demonstrate that, under parameters ensuring the same security level, our optimized G+G variant reduces the signature size by approximately 25%.