Quantum Period Finding against Symmetric Primitives in Practice

TL;DR

This paper demonstrates practical quantum attacks on certain symmetric cryptographic primitives, showing they are vulnerable to quantum algorithms with resources comparable to breaking RSA-2048, and provides optimized quantum circuits for cryptanalysis.

Contribution

First complete implementation of offline Simon's algorithm for cryptanalysis, with optimized quantum circuits and the most efficient known attacks on PRINCE and Chaskey.

Findings

Quantum attacks require qubits comparable to RSA-2048.

Attacks on PRINCE and Chaskey are the most efficient to date.

Elephant scheme is less vulnerable due to smaller key size.

Abstract

We present the first complete implementation of the offline Simon's algorithm, and estimate its cost to attack the MAC Chaskey, the block cipher PRINCE and the NIST lightweight candidate AEAD scheme Elephant. These attacks require a reasonable amount of qubits, comparable to the number of qubits required to break RSA-2048. They are faster than other collision algorithms, and the attacks against PRINCE and Chaskey are the most efficient known to date. As Elephant has a key smaller than its state size, the algorithm is less efficient and ends up more expensive than exhaustive search. We also propose an optimized quantum circuit for boolean linear algebra as well as complete reversible implementations of PRINCE, Chaskey, spongent and Keccak which are of independent interest for quantum cryptanalysis. We stress that our attacks could be applied in the future against today's communications, and recommend caution when choosing symmetric constructions for cases where long-term security is expected.