International Association for Cryptologic Research

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Paper: Compact Implementations of Rainbow and UOV using AVX2

Authors:
Kyung-Ah Shim , NIMS
Sangyub Lee , NIMS
Namhun Koo , Ewha Womans University
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Abstract: Recently, a signature scheme based on multivariate quadratic equations, Rainbow, was selected as one of digital signature finalists for NIST Post-Quantum Cryptography Standardization Round 3. Signing and verification of Rainbow are the fastest among post-quantum signature schemes at most security levels, but the higher the security level, the slower the performance. Furthermore, the parameters of Rainbow are getting bigger due to improved MinRank attacks and Rainbow Band Separation attacks. % and the Rainbow Band Separation attack. In this paper, we provide compact implementations of Rainbow and UOV using AVX2 instructions set. These compact implementations include several optimizations for signing to accelerate solving linear systems and the Vinegar value substitution. A new block matrix inversion (BMI) method using the Lower-Diagonal-Upper decomposition of blocks matrices based on the Schur complement accelerates solving linear systems. Compared to UOV implemented with Gaussian elimination, our implementations with the BMI result in speedups of 12.36\%, 24.3\% and 34\% for signing at security categories I, III and V, respectively. Compared to Rainbow implemented with Gaussian elimination, our implementations with the BMI result in speedups of 16.13\% and 20.73\% at the security categories III and V, respectively. We show that precomputations for the Vinegar value substitution and solving linear systems dramatically improve their signing. UOV with precomputation is 16.9 times, 35.5 times and 62.8 times faster than UOV without precomputation at the three security categories, respectively. Rainbow with precomputation is 2.1 times}, 2.2 times and 2.8 times faster than Rainbow without precomputation at the three security categories, respectively. We then investigate resilience against leakage or reuse of the precomputed values in UOV and Rainbow to use the precomputation securely: the leakage or reuse of the precomputed values leads to their full secret key recoveries in polynomial-time.
BibTeX
@article{tches-2022-31632,
  title={Compact Implementations of Rainbow and UOV using AVX2},
  journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
  publisher={RUB},
  author={Kyung-Ah Shim and Sangyub Lee and Namhun Koo},
  year=2022
}