A practical-time related-key attack on the KASUMI cryptosystem used in GSM and 3G telephony

Over the last 20 years, the privacy of most GSM phone conversations was protected by the A5/1 and A5/2 stream ciphers, which were repeatedly shown to be cryptographically weak. They are being replaced now by the new A5/3 and A5/4 algorithms, which are based on the block cipher KASUMI. In this paper we describe a new type of attack called a sandwich attack, and use it to construct a simple related-key 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 with a related-key attack which uses only 4 related keys, 2 ²⁶ data, 2³⁰ bytes of memory, and 2³² time. These completely practical complexities were experimentally verified by performing the attack in less than two hours on a single-core of a PC. Interestingly, neither our technique nor any other published attack can break the original MISTY block cipher (on which KASUMI is based) significantly faster than exhaustive search. Our results thus indicate that the modifications made by ETSI's SAGE group in moving from MISTY to KASUMI made it extremely weak when related-key attacks are allowed, but do not imply anything about its resistance to single-key attacks. Consequently, there is no indication that the way KASUMI is implemented in GSM and 3G networks is practically vulnerable in any realistic attack model.