We proposed some improvements, new tradeoffs between classical and quantum time and memory, and extended their scope of applications to cases where only a classical oracle is available.In cryptanalysis, in symmetric cryptography, we proposed some attacks against symmetric constructions based on hidden shifts, and generalized many attacks using hidden periods to cases where the construction is only accessible classically. In quantum computing, we studied the hidden period and hidden shift problems, which are among the few known problems that have some applications in cryptogaphy and for which the best known quantum algorithm is more than polynomially faster than the best known classical algorithm. In this thesis, we study the security of cryptographic systems against an adversary who has access to a quantum computer. It further illustrates that the block cipher that is proved to be safe under classical settings is not necessarily secure under quantum conditions. The attack results show that adding round constants does not completely improve the security of the ciphers, and quantum attacks can provide an exponential speed-up over the same attacks in the classical model. As for quantum attacks, by improving on existing quantum attack methods we demonstrate a quantum single-key slide attack on LED-64 and a quantum related-key attack on LED- 128, and indicators of the two attack algorithms are analyzed in detail. The analysis result shows that LED-64 is unable to resist this kind of classical slide attack, but that attack method is not applicable to LED-128. By analyzing the information leakage of round constants, we can introduce the differential of the round constants to propose a classical slide attack on full-round LED-64 with a probability of 1. In this paper, based on the basic principles of classical slide attacks and Simon’s algorithm, we take LED-like lightweight block ciphers as research objects to present a security analysis under both classical and quantum attacks, fully considering the influence on the security of the ciphers of adding the round constants. Correspondingly, there is a need to study whether the symmetric cryptosystem can still guarantee high security with the advent of quantum computers. Asymmetric cryptographic schemes, represented by RSA, have been shown to be insecure under quantum computing conditions.
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