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Due to Shor's algorithm, quantum computers are a severe threat for public keycryptography. This motivated the cryptographic community to search forquantum-safe solutions. On the other hand, the impact of quantum computing onsecret key cryptography is much less understood. In this paper, we considerattacks where an adversary can query an oracle implementing a cryptographicprimitive in a quantum superposition of different states. This model gives alot of power to the adversary, but recent results show that it is nonethelesspossible to build secure cryptosystems in it.  We study applications of a quantum procedure called Simon's algorithm (thesimplest quantum period finding algorithm) in order to attack symmetriccryptosystems in this model. Following previous works in this direction, weshow that several classical attacks based on finding collisions can bedramatically sped up using Simon's algorithm: finding a collision requires$\Omega(2^{n/2})$ queries in the classical setting, but when collisions happenwith some hidden periodicity, they can be found with only $O(n)$ queries in thequantum model.  We obtain attacks with very strong implications. First, we show that the mostwidely used modes of operation for authentication and authenticated encryptione.g. CBC-MAC, PMAC, GMAC, GCM, and OCB) are completely broken in this securitymodel. Our attacks are also applicable to many CAESAR candidates: CLOC, AEZ,COPA, OTR, POET, OMD, and Minalpher. This is quite surprising compared to thesituation with encryption modes: Anand et al. show that standard modes aresecure 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 cryptanalysistechnique in the quantum model.

Breaking Symmetric Cryptosystems using Quantum Period Finding