密码体制的量子算法分析

Quantum Analysis of Modern Cryptosystems

很多快速量子算法都可以归结为隐子群问题的讨论,本文回顾了隐子群问题量子算法的基本思想,分析了群上量子算法的优越性。分析了可以归结为隐于群问题的公钥密码体制,描述了求解椭圆曲线上离散对数问题的量子算法,讨论了隐子群问题量子算法的局限性。

Many fast quantum algorithms,which cannot be solved efficiently by classical probabilistic algorithms,can be reduced to the discussion of hidden subgroup problems. The quantum algorithms of hidden subgroup problems are reviewed and the advantages of quantum algorithm over group are analyzed in the paper. This paper surveys the mod- ern cryptosystems that can be broken by quantum hidden subgroup algorithms in polynomial time. Limits of the hid- den subgroup problems quantum algorithms are also discussed.