fixed-point-arithmetic

The article describes a new implementation of the Falcon signature scheme that replaces floating-point arithmetic with fixed-point arithmetic, enhancing security and efficiency as presented in a CRYPTO 2026 paper.

This paper analyzes generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces with deterministic or stochastic rounding, showing that rounding degrades generalization for GD and introduces dimension-dependent errors for stochastic rounding.