Optimized Lattice Basis Reduction In Dimension 2, and Fast Schnorr and EdDSA Signature Verification

Abstract

We present an optimization of Lagrange\u27s algorithm for lattice basis reduction in dimension 2. The optimized algorithm is proven to be correct and to always terminate with quadratic complexity; it uses more iterations on average than Lagrange\u27s algorithm, but each iteration is much simpler to implement, and faster. The achieved speed is such that it makes application of the speed-up on ECDSA and EC Schnorr signatures described by Antipa et al worthwhile, even for very fast curves such as Ed25519. We applied this technique to signature verification in Curve9767, and reduced verification time by 30 to 33% on both small (ARM Cortex M0+ and M4) and large (Intel Coffee Lake with AVX2) architectures