Asymmetric cryptographic schemes represented by RSA have been shown to be insecure under the condition of quantum computers.Correspondingly,whether the symmetric cryptosystem can still ensure its high security under the condition of quantum computers is a problem that needs to be studied.In this paper,based on the basic principles of classical slide attack and Simons algorithm,we take the LED-like lightweight block ciphers as the research objects to present the security analysis under classical and quantum attacks,fully considering the influence of adding the round constants on the security of the ciphers.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.The analysis result shows that LED-64 is unable to resist this kind of classical slide attack,but this attack method is not applicable to LED-128.As for quantum attack,by improving the existing quantum attack methods,we give quantum single-key slide attack on LED-64 and quantum related-key attack on LED-128,respectively,and indicators of the two attack algorithms are analyzed in detail.The attack results show that adding round constants does not completely improve the security of the ciphers and quantum attacks can be exponentially speed-up over the same attacks in the classical model.It further illustrates that the block cipher that is proved to be safe under classical settings is not necessarily secure under quantum computers.