Open AccessIterative Block Ciphers from Tweakable Block Ciphers with Long Tweaks
Author(s) -
Ryota Nakamichi,
Tetsu Iwata
Publication year - 2020
Publication title -
iacr transaction on symmetric cryptology
Language(s) - English
Resource type - Journals
ISSN - 2519-173X
DOI - 10.46586/tosc.v2019.i4.54-80
Subject(s) - block cipher , computer science , block (permutation group theory) , simple (philosophy) , cbc mac , theoretical computer science , computer security , mathematics , cryptography , combinatorics , philosophy , epistemology
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.