Lower Bounds for Leakage-Resilient Secret-Sharing Schemes against Probing Attacks

• Published in: 2021 IEEE International Symposium on Information Theory (ISIT) pp. 976 - 981
• Main Authors: Adams, Donald Q., Maji, Hemanta K., Nguyen, Hai H., Nguyen, Minh L., Paskin-Cherniavsky, Anat, Suad, Tom, Wang, Mingyuan
• Format: Conference Proceeding
• Language: English
• Published: IEEE 12.07.2021
• Subjects: Additives; Computational modeling; Cryptography; Hardware; Information theory; Probability distribution; Side-channel attacks
• DOI: 10.1109/ISIT45174.2021.9518230

Historically, side-channel attacks have revealed partial information about the intermediate values and secrets of computations to compromise the security of cryptographic primitives. The objective of leakage-resilient cryptography is to model such avenues of information leakage and study techniques to realize them securely. This work studies the local leakage-resilience of prominent secret-sharing schemes like Shamir's secret-sharing scheme and the additive secret-sharing scheme against probing attacks that leak physical-bits from the memory hardware storing the secret shares. Consider the additive secret-sharing scheme among k parties over a prime field such that the prime needs \lambda -bits for its binary representation, where \lambda is the security parameter. We prove that k must be at least \omega(\log\lambda/\log\log\lambda) for the scheme to be secure against even one physical-bit leakage from each secret share. This result improves the previous state-of-the-art result where an identical lower bound was known for one-bit general leakage from each secret share (Benhamouda, Degwekar, Ishai, and Rabin, CRYPTO-2018). This lower bound on the reconstruction threshold extends to Shamir's secret-sharing scheme if one does not carefully choose the evaluation places for generating the secret shares. For this scheme, our result additionally improves another lower bound on the reconstruction threshold k of Shamir's secret-sharing scheme (Nielsen and Simkin, EUROCRYPT-2020) when the total number of parties is \mathcal{O}(\lambda\log\lambda/\log\log\lambda) . Our work provides the analysis of the recently-proposed (explicit) physical-bit leakage attack of Maji, Nguyen, Paskin-Cherniavsky, Suad, and Wang (EUROCRYPT-2021), namely the "parity of parity" attack. This analysis relies on lower-bounding the "discrepancy" of the Irwin-Hall probability distribution.