Quantum Chosen-Ciphertext Attacks against Feistel Ciphers

Seminal results by Luby and Rackoff show that the 3-round Feistel cipher is secure against chosen-plaintext attacks (CPAs), and the 4-round version is secure against chosen-ciphertext attacks (CCAs). However, the security significantly changes when we consider attacks in the quantum setting, where the adversary can make superposition queries. By using Simon’s algorithm that detects a secret cycle-period in polynomial-time, Kuwakado and Morii showed that the 3-round version is insecure against quantum CPA by presenting a polynomial-time distinguisher. Since then, Simon’s algorithm has been heavily used against various symmetric-key constructions. However, its applications are still not fully explored.

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