Iterative Block Ciphers from Tweakable Block Ciphers with Long Tweaks
Keywords:Beyond-birthday-bound security, Tweakable block cipher, Coefficient-H technique, Provable security
We consider a problem of constructing a secure block cipher from a tweakable block cipher (TBC) with long tweaks. Given a TBC with n-bit blocks and Γn-bit tweaks for Γ ≥ 1, one of the constructions by Minematsu in DCC 2015 shows that a simple iteration of the TBC for 3d rounds yields a block cipher with dn-bit blocks that is secure up to 2dn/2 queries, where d = Γ + 1.
In this paper, we show three results.
1. Iteration of 3d − 2 rounds is enough for the security up to 2dn/2 queries, i.e., the security remains the same even if we reduce the number of rounds by two.
2. When the number of queries is limited to 2n, d+1 rounds are enough, and with d + l rounds for 1 ≤ l ≤ d − 1, the security bound improves as l grows.
3. A d-round construction gives a block cipher secure up to 2n/2 queries, i.e., it achieves the classical birthday-bound security.
Our results show that a block cipher with beyond-birthday-bound (BBB) security (with respect to n) is obtained as low as d + 1 rounds, and we draw the security spectrum of d + l round version in the range of 1 ≤ l ≤ d−1 and l = 2d−2 for BBB security, and l = 0 for birthday-bound security.
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Copyright (c) 2020 Ryota Nakamichi, Tetsu Iwata
This work is licensed under a Creative Commons Attribution 4.0 International License.