2 results sorted by ID
Possible spell-corrected query: Random Punctured need-Solomon code
BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes
Hadas Zeilberger, Binyi Chen, Ben Fisch
Cryptographic protocols
This works introduces Basefold, a new $\textit{field-agnostic}$ Polynomial Commitment Scheme (PCS) for multilinear polynomials that has $O(\log^{2}(n))$ verifier costs and $O(n \log n)$ prover time. An important application of a multilinear PCS is constructing Succinct Non-interactive Arguments (SNARKs) from multilinear polynomial interactive oracle proofs (PIOPs). Furthermore, field-agnosticism is a major boon to SNARK efficiency in applications that require (or benefit from) a certain...
Leakage-resilience of the Shamir Secret-sharing Scheme against Physical-bit Leakages
Hemanta K. Maji, Hai H. Nguyen, Anat Paskin-Cherniavsky, Tom Suad, Mingyuan Wang
Foundations
Efficient Reed-Solomon code reconstruction algorithms, for example, by Guruswami and Wootters (STOC--2016), translate into local leakage attacks on Shamir secret-sharing schemes over characteristic-2 fields. However, Benhamouda, Degwekar, Ishai, and Rabin (CRYPTO--2018) showed that the Shamir secret sharing scheme over prime-fields is leakage resilient to one-bit local leakage if the reconstruction threshold is roughly 0.87 times the total number of parties. In several application scenarios,...
This works introduces Basefold, a new $\textit{field-agnostic}$ Polynomial Commitment Scheme (PCS) for multilinear polynomials that has $O(\log^{2}(n))$ verifier costs and $O(n \log n)$ prover time. An important application of a multilinear PCS is constructing Succinct Non-interactive Arguments (SNARKs) from multilinear polynomial interactive oracle proofs (PIOPs). Furthermore, field-agnosticism is a major boon to SNARK efficiency in applications that require (or benefit from) a certain...
Efficient Reed-Solomon code reconstruction algorithms, for example, by Guruswami and Wootters (STOC--2016), translate into local leakage attacks on Shamir secret-sharing schemes over characteristic-2 fields. However, Benhamouda, Degwekar, Ishai, and Rabin (CRYPTO--2018) showed that the Shamir secret sharing scheme over prime-fields is leakage resilient to one-bit local leakage if the reconstruction threshold is roughly 0.87 times the total number of parties. In several application scenarios,...