Cryptanalysis of Tiny Encryption Algorithm Based on SMT Solvers Using HPC

Abstract

Tiny Encryption Algorithm (TEA) is a block cipher algorithm that uses symmetric key of 128-bits. It performs 32 rounds for encryption/decryption. TEA uses addition modulo $2^{32}$, XoR, and shift operations in its algorithm. We convert TEA algorithm into nonlinear system of equations and solve the system using Satisfiability Modulo Theory solvers (SMT) on a desktop computer and also on high performance computing (HPC) facility. As solving system of equations is NP-complete problem, we tried solving the system for various number of rounds out of 32 rounds. The solver $Z_3 (py)$, a Satisfiability Modulo Theories (SMT) solver, has been chosen to perform algebraic cryptanalysis. We could solve the system up to 5^th round and found the actual secret key successfully among few solutions of high probable keys which we got from solver with in 15,576.34 min using HPC. Nonlinearity will increase as number of round increases, so solving high nonlinear system is very difficult. Our aim is to solve a specific kind of nonlinear system of equations. We tried to recover the partial keys for rounds greater than 5. Results of the key recovery are present in this paper.