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Paper 2024/1875

mUOV: Masking the Unbalanced Oil and Vinegar Digital Sigital Signature Scheme at First- and Higher-Order

Abstract

The National Institute for Standards and Technology (NIST) initiated a standardization procedure for additional digital signatures and recently announced round-2 candidates for the PQ additional digital signature schemes. The multivariate digital signature scheme Unbalanced Oil and Vinegar (UOV) is one of the oldest post-quantum schemes and has been selected by NIST for Round 2. Although UOV is mathematically secure, several side-channel attacks (SCA) have been shown on the UOV or UOV-based digital signatures. We carefully analyze the sensitivity of variables and operations in the UOV scheme from the side-channel perspective and show which require protection. To mitigate implementation-based SCA, we integrate a provably secure arbitrary-order masking technique with the key generation and signature generation algorithms of UOV. We propose efficient techniques for the masked dot-product and matrix-vector operations, which are both critical in multivariate DS schemes. We also implemented and demonstrate the practical feasibility of our masking algorithms for UOV-Ip on the ARM Cortex-M4 microcontroller. Our first-order masked UOV implementations have $2.7\times$ and $3.6\times$ performance overhead compared to the unmasked scheme for key generation and signature generation algorithms. Our first-order masked UOV implementations use $1.3\times$ and $1.9\times$ stack memory rather than the unmasked version of the key generation and signature generation algorithms.