Processing Time Optimization for XMSS on an Object Oriented SPHINCS+ Implementation

Abstract

Computation paradigms are changing due to the idea of quantum computers. Although today this kind of technology is not available and has not reached its full potential, public-key cryptography is at risk since its security depends on problems that classical computers cannot solve in polynomial time, while quantum computers can. Quantum resistant cryptography has been developed for years and this work proposes a new implementation that reduces the processing time of XMSS signature generation of SPHINCS+, a stateless scheme designed for digital signature and is in process of standardization by the National Institute of Standards and Technology of the United States. The proposed implementation has a tradeoff between time and memory space. While original documentation is focused on space optimization, this new implementation needs additional 20 kB of memory for each tree during the signing process in order to generate a signature, but optimizes the time the internal process requires in the authentication path generation, from exponential to linear complexity. Digital signatures generated by both ways are the same.