Witness Encryption via Prime-Order Generic Groups

2026-09-16

AI Summary

该研究使用素数阶循环群在经典通用群模型中无条件构建了NP的见证加密方法，解决了SAT实例的加密与解密问题。

Abstract

We unconditionally construct witness encryption for NP in the classical generic-group model, using an ordinary cyclic group of prime order. For SAT instances of size $n$, the encryption algorithm runs in time poly$(n)$, and any satisfying assignment can be used to decrypt in poly$(n)$ time with correctness error $2^{-n^{Ω(1)}}$. If no satisfying assignment exists, then every generic adversary making at most $n^{Θ(\log n)}$ group queries has distinguishing advantage at most $n^{-Θ(\log n)}$. Along the way, we prove the first superconstant-factor NP-hardness of approximation result for homogeneous MinRank under randomized polynomial-time reductions, achieving a logarithmic gap even when the rank-one witness has a Boolean right factor.

Problem

• Witness Encryption
• NP-hardness
• Generic Groups

Innovation

• Witness Encryption
• Prime-Order Generic Groups
• NP-hardness of Approximation
• Homogeneous MinRank