New Security Proofs and Complexity Records for Advanced Encryption Standard

Abstract

Common block ciphers like AES specified by the NIST or KASUMI (A5/3) of GSM are extensively utilized by billions of individuals globally to protect their privacy and maintain confidentiality in daily communications. However, these ciphers lack comprehensive security proofs against the vast majority of known attacks. Currently, security proofs are limited to differential and linear attacks for both AES and KASUMI. For instance, the consensus on the security of AES is not based on formal mathematical proofs but on intensive cryptanalysis over its reduced rounds spanning several decades. In this work, we introduce new security proofs for AES against another attack method: impossible differential (ID) attacks. We classify ID attacks as reciprocal and nonreciprocal ID attacks. We show that sharp and generic lower bounds can be imposed on the data complexities of reciprocal ID attacks on substitution permutation networks. We prove that the minimum data required for a reciprocal ID attack on AES using a conventional ID characteristic is 2(66) chosen plaintexts whereas a nonreciprocal ID attack involves at least 2(88) computational steps. We mount a nonreciprocal ID attack on 6-round AES for 192-bit and 2(56)-bit keys, which requires only 2(18) chosen plaintexts and outperforms the data complexity of any attack. Given its marginal time complexity, this attack does not pose a substantial threat to the security of AES. However, we have made enhancements to the integral attack on 6-round AES, thereby surpassing the longstanding record for the most efficient attack after a period of 23 years.