In 2002, Murphy and Robshaw introduced an extension BES of AES and argued this could compromise the security of AES. We intro-duce here two block-ciphers CES and Big-BES that are some extensions of the AES and BES respectively in the spirit of Hensel lifting extensions. They are denned similarly to the AES respectively BES except that every operations are performed in a ring structure including the field GF(2~8). We show that the AES and BES can be embedded in their extensions. More precisely, by restricting these extensions on a given subset, we obtain a fully equivalent description of the AES and BES. Furthermore, we show that these natural extensions are trivially weak by describing a cryptanalysis of them despite it leads to no consequence about the security of AES or BES. This shows that (except the nice mathematical construction) the Murphy-Robshaw extension might be pointless.
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