FDH、PFDH及GPV-IBE的紧致后量子证明  

Tighter Post-Quantum Proof for Plain FDH,PFDH,and GPV-IBE

作　　者：刘羽 江浩东 赵运磊 LIU Yu;JIANG Hao-Dong;ZHAO Yun-Lei(School of Computer Science,Fudan University,Shanghai 200433,China;Henan Key Laboratory of Network Cryptography Technology,Zhengzhou 450001,China;State Key Laboratory of Cryptology,Beijing 100878,China)

机构地区：[1]复旦大学计算机科学技术学院,上海200433 [2]河南省网络密码技术重点实验室,郑州450001 [3]密码科学技术全国重点实验室,北京100878

出　　处：《密码学报(中英文)》2025年第1期148-162,共15页Journal of Cryptologic Research

基　　金：国家重点研发计划(2022YFB2701601);国家自然科学基金(62002385);密码科学技术全国重点实验室面上课题(MMKFKT202227);上海市科委技术标准基金(21DZ2200500);上海市协同创新基金(XTCX-KJ-2023-54);上海市科委区块链关键技术攻关专项基金(23511100300)。

摘　　要：在CRYPTO 2012中,Zhandry开发了通用的半恒定预言机技术,并在量子随机预言机模型下证明了基于身份的加密方案GPV-IBE和全域哈希(FDH)签名方案的安全性.然而,Zhandry提供的归约证明其损失是二次的.本文给出量子RO模型下关于FDH、概率FDH和GPV-IBE的更紧致的线性损失的安全性证明.本文证明基于Don等开发的测量后重编程技术,还为量子RO模型下的确定性哈希-签名范式提供了安全证明,条件是其中原像采样函数不可逆.该结果可以直接应用于Falcon及其变体的确定性版本.At CRYPTO 2012,Zhandry developed generic semi-constant oracle technique and proved security of an identity-based encryption scheme,GPV-IBE,and full domain hash(FDH)signature scheme in the quantum random oracle model(QROM).However,the reduction provided by Zhandry incurred a quadratic reduction loss.This study provides a much tighter proof,with linear reduction loss,for the FDH,probabilistic FDH(PFDH),and GPV-IBE in the QROM.The proof is based on the measure-and-reprogram technique developed by Don et al.A security proof is also given for the deterministic hash-and-sign in the QROM,assuming the underlying PSF is non-invertible.This result can be applied to the deterministic version of Falcon and its variants.

关 键 词：量子随机预言机 全域哈希 基于身份的加密方案 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]