摘要
在STOC 2009上,Dodis,Kalai和Lovett研究了(静态的)带有指数级难以求逆辅助输入的LPN(Learning Parity with Noise)问题的困难性,他们通过引入一个新的假设(被称为带噪声的子空间学习问题,Learning Subspace with Noise)证明了LPN问题在高噪声条件下是准多项式(quasi-polynomial)困难的,然而他们的结果并未在LPN的标准假设下得到证明.本文将介绍Yu(ePrint 2009/467)以及Goldwasser等人在ITCS 2010上提出的"从子空间中取样(sampling from subspace)"技术,利用该技术Yu等人(CRYPTO 2016)证明了标准LPN蕴含了一种新的健壮的(抗泄漏)工作模式.换而言之,常量噪声(constant-noise)的LPN在带有亚指数级难以求逆的辅助输入时仍具有与标准LPN假设下可比拟的安全性.更进一步,在亚指数级困难(即(?)),n为密钥大小)常量噪声LPN假设下,Yu等人(CRYPTO 2016)基于poly-logarithmic熵源得到一种LPN问题变体,并进一步构造CPA/CCA安全公钥加密(PKE)方案和不经意传输(oblivious transfer,OT)协议,从而证明了标准LPN蕴含公钥加密.在此之前(特别是自Alekhnovich发表在FOCS 2003的工作以来),如何在常量噪声LPN假设下构造PKE和OT—直是未解决的公开问题.
Dodis, Kalai and Lovett(STOC 2009) initiated the study of the Learning Parity with Noise(LPN) problem with(static) exponentially hard-to-invert auxiliary input. In particular, they showed that under a new assumption(called Learning Subspace with Noise) the above is quasi-polynomially hard in the high(polynomially close to uniform) noise regime. Based on the 'sampling from subspace'technique by Yu(eprint 2009/467) and Goldwasser et al.(ITCS 2010), standard LPN can work in a mode(reducible to itself) where the constant-noise LPN(by sampling its matrix from a random subspace) is robust against sub-exponentially hard-to-invert auxiliary input with comparable security to the underlying LPN. Under constant-noise LPN with certain sub-exponential hardness(i.e., 2^(ω(n^(1/2))))for secret size n), a variant of the LPN with security on poly-logarithmic entropy sources is obtained,which in turn implies CPA/CCA secure public-key encryption(PKE) schemes and oblivious transfer(OT) protocols. Prior to this, basing PKE and OT on constant-noise LPN had been an open problem since Alekhnovich's work(FOCS 2003).
出处
《密码学报》
CSCD
2017年第5期506-516,共11页
Journal of Cryptologic Research
基金
国家自然科学基金项目(61472249
61572192
61571191)
陕西省国际科技合作与交流计计划(2016KW-038)
