A Practical-Time Related-Key Attack on the KASUMI Cryptosystem Used in GSM and 3G Telephony

Abstract

The privacy of most GSM phone conversations is currently protected by the 20+ years old A5/1 and A5/2 stream ciphers, which were repeatedly shown to be cryptographically weak. They will soon be replaced by the new A5/3 (and the soon to be announced A5/4) algorithm based on the block cipher KASUMI, which is a modified version of MISTY. In this paper we describe a new type of attack called a sandwich attack, and use it to construct a simple distinguisher for 7 of the 8 rounds of KASUMI with an amazingly high probability of 2− 14. By using this distinguisher and analyzing the single remaining round, we can derive the complete 128 bit key of the full KASUMI by using only 4 related keys, 226 data, 230 bytes of memory, and 232 time. These complexities are so small that we have actually simulated the attack in less than two hours on a single PC, and experimentally verified its correctness and complexity. Interestingly, neither our technique nor any other published attack can break MISTY in less than the 2128 complexity of exhaustive search, which indicates that the changes made by ETSI’s SAGE group in moving from MISTY to KASUMI resulted in a much weaker cipher.