Paper 2024/1614 Original: eprint.iacr.org/2024/1614 ↗

Related-Key Cryptanalysis of FUTURE

Abstract

At Africacrypt 2022, Gupta et al. introduced FUTURE, a 64-bit lightweight block cipher based on an MDS matrix and designed in an SPN structure, with a focus on achieving single-cycle encryption and low implementation cost, especially in unrolled architectures. While the designers evaluated its security under various attack models, they did not consider related-key cryptanalysis. In this work, we address this gap by analyzing the security of FUTURE in the related-key setting using techniques based on Mixed Integer Linear Programming (MILP). We first propose a simplified and generalizable approach for applying MILP to model any MDS or near-MDS-based cipher that follows the substitution-permutation paradigm. Using our MILP framework, we construct an 8-round related-key distinguisher on FUTURE, requiring $2^{58}$ plaintexts, $2^{58}$ \xor operations, and negligible memory. We further identify a full-round (i.e., 10 rounds) boomerang distinguisher with a probability of $2^{-45.8}$, enabling a distinguishing attack with $2^{48}$ data and time complexity. In addition, we develop a full-round key recovery attack on FUTURE with data, time, and memory complexities of $2^{18}$, $2^{70}$, and $2^{64}$, respectively. Although all known single-key attacks remain impractical (with time complexities of at least $2^{112}$), our results demonstrate a full-round cryptanalysis of FUTURE in the related-key setting, thereby challenging its claimed security guarantees.