Research On New Quantum Algorithm Attack Model Based On Symmetric Cryptosystem

In this era of information explosion,more and more people pay attention to information security.Moreover,with the continuous development of quantum computing technology,re-searchers have also begun to think about the security of existing cryptography in the future quantum world,and prepare for the future.For this reason,not only post-quantum ciphers that can withstand quantum attacks have been proposed,but also the cryptanalysis with the help of quantum computing would be proposed.Among them,cryptanalysis based on quantum algo-rithms,compared with classical cryptanalysis,can have a significant acceleration effect on some specific problems or specific cipher structures,and can even accelerate exponentially.There-fore,the combination of quantum computing and cryptanalysis is a win-win situation.It can not only prove whether the existing cryptography is safe in the quantum world,but also promote the development of post-quantum cryptography.This paper studies quantum attack models on common authenticated encryption algorithms and Feistel structure,with the main purpose of reducing time complexity.The specific research contents are as follows:（1）Since the classic forgery attacks on COPA,AES-COPA and Marble authenticated en-cryption algorithms need to query about 2^n/2times and their success probability are not high.To solve this problem,the corresponding quantum forgery attacks on COPA,AES-COPA and Mar-ble authenticated encryption algorithms are presented.In the quantum forgery attacks on COPA and AES-COPA,our attack uses Simon’s algorithm to find the period of the tag generation func-tion in COPA and AES-COPA by querying in superposition,and then generate a forged tag for a new message.While in the quantum forgery attack on Marble,Simon’s algorithm is used to recover the secret parameter L,and the forged tag can be computed with L.Compared with classic forgery attacks on COPA,AES-COPA and Marble,our attack can reduce the number of queries from O(2^n/2)to O（n）and improve success probability close to 100%.（2）In order to reduce the time complexity of quantum attacks on 7-round Feistel construc-tion,a quantum meet-in-the-middle attack which combinines quantum Claw Finding algorithm and 5-round distinguisher is proposed.The attack is divided into two phases,online query phase and offline calculation phase.In the online query phase,the eligible plaintext pairs and corre-sponding ciphertexts are collected,and the difference sequence in the left half of the 6th round is calculated for each pair of plaintexts.In the offline calculation phase,according to the 5-round discriminator,the difference sequence of the left half of the 5th round of the 5-round discrimi-nator is calculated in all cases,and then the quantum Claw Finding algorithm is used to find the equal one between the two difference sequence sets.And the first round key and the seventh round key can be deduced finally.Compared with other quantum attacks or classical attacks,whose time complexity is O（2ⁿ）,the time complexity of our quantum meet-in-the-middle attack requires only O(2^7n/8).