Paper 2020/1076

Minimizing the Two-Round Tweakable Even-Mansour Cipher

Avijit Dutta

Abstract

In CRYPTO 2015, Cogliati et al. have proposed one-round tweakable Even-Mansour (\textsf{1-TEM}) cipher constructed out of a single $$-bit public permutation $$ and a uniform and almost XOR-universal hash function \textsf{H} as $$, where $$ is the tweak, and $$ is the $$-bit message. Authors have shown that its two-round extension, which we refer to as \textsf{2-TEM}, obtained by cascading $$-independent instances of the construction gives $$-bit security and $$-round cascading gives $$-bit security. In ASIACRYPT 2015, Cogliati and Seurin have shown that four-round tweakable Even-Mansour cipher, which we refer to as \textsf{4-TEM}, constructed out of four independent $$-bit permutations $$ and two independent $$-bit keys $$, defined as $$ is secure upto $$ adversarial queries. In this paper, we have shown that if we replace two independent permutations of \textsf{2-TEM} (Cogliati et al., CRYPTO 2015) with a single $$-bit public permutation, then the resultant construction still guarrantees security upto $$ adversarial queries. Using the results derived therein, we also show that replacing the permutation $$ with $$ in the above equation preserves security upto $$ adversarial queries.