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SPHINCS-Simpira: Fast Stateless Hash-based Signatures with Post-quantum Security



Shay Gueron, Nicky Mouha


We introduce SPHINCS-Simpira, which is a variant of the SPHINCS signature scheme with Simpira as a building block. SPHINCS was proposed by Bernstein et al. at EUROCRYPT 2015 as a hash-based signature scheme with post-quantum security. At ASIACRYPT 2016, Gueron and Mouha introduced the Simpira family of cryptographic permutations, which delivers high throughput on modern 64-bit processors by using only one building block: the AES round function. The Simpira family claims security against structural distinguishers with a complexity below 2^128 using classical computers. In this document, we explain why the same claim can be made against quantum computers as well. Although Simpira follows a very conservative design strategy, our benchmarks show that SPHINCS-Simpira provides a 1.5x speed-up for key generation, a 1.4x speed-up for signing 59-byte messages, and a 2.0x speed-up for verifying 59-byte messages compared to the originally proposed SPHINCS-256.
Cryptology ePrint Archive


Simpira, SPHINCS, post-quantum security, hash-based signature, AES-NI


Gueron, S. and Mouha, N. (2017), SPHINCS-Simpira: Fast Stateless Hash-based Signatures with Post-quantum Security, Cryptology ePrint Archive, [online],, (Accessed July 15, 2024)


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Created June 28, 2017, Updated October 12, 2021