International Association for Cryptologic Research (IACR)
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