International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: 4-Round Luby-Rackoff Construction is a qPRP

Akinori Hosoyamada
Tetsu Iwata
DOI: 10.1007/978-3-030-34578-5_6
Search ePrint
Search Google
Abstract: The Luby-Rackoff construction, or the Feistel construction, is one of the most important approaches to construct secure block ciphers from secure pseudorandom functions. The 3- and 4-round Luby-Rackoff constructions are proven to be secure against chosen-plaintext attacks (CPAs) and chosen-ciphertext attacks (CCAs), respectively, in the classical setting. However, Kuwakado and Morii showed that a quantum superposed chosen-plaintext attack (qCPA) can distinguish the 3-round Luby-Rackoff construction from a random permutation in polynomial time. In addition, Ito et al. recently showed a quantum superposed chosen-ciphertext attack (qCCA) that distinguishes the 4-round Luby-Rackoff construction. Since Kuwakado and Morii showed the result, a problem of much interest has been how many rounds are sufficient to achieve provable security against quantum query attacks. This paper answers to this fundamental question by showing that 4-rounds suffice against qCPAs. Concretely, we prove that the 4-round Luby-Rackoff construction is secure up to $$O(2^{n/12})$$ quantum queries. We also give a query upper bound for the problem of distinguishing the 4-round Luby-Rackoff construction from a random permutation by showing a distinguishing qCPA with $$O(2^{n/6})$$ quantum queries. Our result is the first to demonstrate the security of a typical block-cipher construction against quantum query attacks, without any algebraic assumptions. To give security proofs, we use an alternative formalization of Zhandry’s compressed oracle technique.
  title={4-Round Luby-Rackoff Construction is a qPRP},
  booktitle={Advances in Cryptology – ASIACRYPT 2019},
  series={Advances in Cryptology – ASIACRYPT 2019},
  author={Akinori Hosoyamada and Tetsu Iwata},