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The Square attack as a means of attacking reduced round variants of AES was described in the initial description of the Rijndael block cipher. This attack can be applied to AES, with a relatively small number of chosen plaintext-ciphertext pairs, reduced to less than six rounds in the case of AES-128 and seven rounds otherwise and several extensions to this attack have been described in the literature. In this paper, the authors describe new variants of these attacks that have a smaller time complexity than those present in the literature. Specifically, they demonstrate that the quantity of chosen plaintext-ciphertext pairs can be halved producing the same reduction in the time complexity.
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