(Quantum) Time-Memory-Data Tradeoff Attacks on the SNOW-V Stream Cipher

Abstract

Symmetric cryptosystems (i.e., stream ciphers and block ciphers) have always played an important part in securing the various generations of 3GPP (3rd Generation Partnership Project) mobile telephony systems. The SNOW-V stream cipher, published in September 2019, is the most recent member of the well-known SNOW family of ciphers. It is designed to provide confidentiality and integrity for 5G communications. There have been no time-memory-data tradeoff (TMDTO) attacks on the cipher published so far. By combining with the BSW sampling technique, we propose TMDTO attacks on SNOW-V. The results show that the attacker can mount a TMDTO attack, where none of the online time complexity, the memory complexity and the offline time complexity are bigger than 2256, if the keystream sequences generated by the secret key, together with different IVs, are provided to the attacker. Furthermore, we analyze the security of SNOW-V against quantum TMDTO attacks, and the results show that a quantum TMDTO attack offers, strictly, better online time complexity than Grover’s algorithm, when the available memory space is bigger than 2170.67. These results are helpful in evaluating the security of SNOW-V against (quantum) TMDTO attacks.