By Carlos Cid
The Belgian block cipher Rijndael used to be selected in 2000 through the U.S. governments nationwide Institute of criteria and expertise (NIST) to be the successor to the information Encryption typical. Rijndael used to be thus standardized because the complex Encryption general (AES), that is almost certainly the worlds most vital block cipher. In 2002, a few new analytical ideas have been prompt which could have a dramatic influence at the protection of the AES. latest analytical concepts for block ciphers count seriously on a statistical process, while those new thoughts are algebraic in nature.
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Extra resources for Algebraic Aspects of the Advanced Encryption Standard
Chapter 3 D E S C R I P T I O N OF T H E AES This chapter gives a brief description of the AES and its design rationale. We place a particular emphasis on areas that are most relevant to subsequent chapters. The AES is a block cipher with a block size of 128 bits and a key size of 128, 192, or 256 bits. Wo denote those versions by AES-128, AES-192, and AES-256 respectively. This monograph focuses on AES-128 and we follow the formal description given in FTPS 197 . 1. Structure T h e standard view of the AES is as a series of operations on a square array of 16 bytes [37, 39, 95].
It is then updated by multiplying the column vector by a specified 4x4 matrix over F. i 02 03 S2,i 01 02 j \ '53. J AddRoundKey. ij + ICr^ij+i user-supplied key to give the 16r < Nr) for the AES. In round r, by Bt — i > H; + /C,-,; (0 < i < 15) or (0 < i, J < 3). Key schedule The generation of the AES round keys is straightforward even though three key sizes are supported. Generally speaking, key material is generated recursively, and at each round sufficient key material is extracted to form a 128-bit round key.
65). T h e linear diffusion required by the wide trail strategy is therefore given by the 128x128 matrix CR over GF(2). The algebraic properties of R and C, and hence CR, are directly given by those of R and C. A u g m e n t e d linear diffusion We have seen t h a t the final two parts of the SubBytes operation, namely the GF(2)-linear mapping and the addition of the S-box constant, form an affine operation over GF(2). Furthermore, the diffxision operations of the AES on bytes of the state space, namely Shif tRows and MixColumns, are also linear operations over GF(2).
Algebraic Aspects of the Advanced Encryption Standard by Carlos Cid