利用量子周期发现破解对称密码体制
Breaking Symmetric Cryptosystems using Quantum Period Finding
摘要：
由于Shor的算法，量子计算机对公钥密码术构成了严重威胁。这促使加密社区寻找量子安全的解决方案。另一方面，量子计算对密钥加密的影响却鲜为人知。在本文中，我们考虑攻击对手可以查询一个预言机实现一个加密原语在量子叠加的不同状态。这个模型给了很多的权力，对手，但最近的结果表明，它仍然是可能的，以建立安全的密码系统在it. We研究应用的量子程序称为西蒙的算法（最简单的量子周期发现算法），以攻击对称密码系统在这个模型中。按照以前的工作在这个方向上，我们表明，几个经典的攻击的基础上找到碰撞可以大大加快使用西蒙的算法：找到一个碰撞需要$Ω(2^{n/2})$查询在经典的设置，但当碰撞发生一些隐藏的周期性，它们可以找到只有$O(n)$查询的量子模型。我们得到的攻击具有非常强的含义。首先，我们证明了最广泛使用的认证和认证加密操作模式（例如CBC-MAC，PMAC，GMAC，GCM和OCB）在这个安全模型中完全被破坏。我们的攻击也适用于许多CAESAR候选者：CLOC，AEZ，COPA，OTR，POET，OMD和Minerator。与加密模式的情况相比，这是相当令人惊讶的：Anand等人表明，标准模式在量子安全的PRF下是安全的。其次，我们表明，西蒙的算法也可以应用到幻灯片攻击，导致一个经典的对称密码分析技术在量子模型的指数加速。
英文摘要：
Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key cryptography is much less understood. In this paper, we consider attacks where an adversary can query an oracle implementing a cryptographic primitive in a quantum superposition of different states. This model gives a lot of power to the adversary, but recent results show that it is nonetheless possible to build secure cryptosystems in it. We study applications of a quantum procedure called Simon's algorithm (the simplest quantum period finding algorithm) in order to attack symmetric cryptosystems in this model. Following previous works in this direction, we show that several classical attacks based on finding collisions can be dramatically sped up using Simon's algorithm: finding a collision requires $Ω(2^{n/2})$ queries in the classical setting, but when collisions happen with some hidden periodicity, they can be found with only $O(n)$ queries in the quantum model. We obtain attacks with very strong implications. First, we show that the most widely used modes of operation for authentication and authenticated encryption e.g. CBC-MAC, PMAC, GMAC, GCM, and OCB) are completely broken in this security model. Our attacks are also applicable to many CAESAR candidates: CLOC, AEZ, COPA, OTR, POET, OMD, and Minalpher. This is quite surprising compared to the situation with encryption modes: Anand et al. show that standard modes are secure with a quantum-secure PRF. Second, we show that Simon's algorithm can also be applied to slide attacks, leading to an exponential speed-up of a classical symmetric cryptanalysis technique in the quantum model.
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