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This chapter presents the following content: Number theory, divisibility & GCD, modular arithmetic with integers, Euclid’s algorithm for GCD & inverse, the AES selection process, the details of Rijndael – the AES cipher, looked at the steps in each round out of four AES stages, last two are discussed: MixColumns, AddRoundKey. | Data Security and Encryption (CSE348) Lecture slides by Lawrie Brown for “Cryptography and Network Security”, 5/e, by William Stallings, briefly reviewing the text outline from Ch 0, and then presenting the content from Chapter 1 – “Introduction”. Lecture # 10 Review The AES selection process The details of Rijndael – the AES cipher looked at the steps in each round Out of four AES stages, two are discussed Substitute bytes Shift Rows Chapter 5 summary. Mix Columns Each column is processed separately Each byte is replaced by a value dependent on all 4 bytes in the column Effectively a matrix multiplication in GF(28) using prime poly m(x) =x8+x4+x3+x+1 The forward mix column transformation, called MixColumns, operates on each column individually. Each byte of a column is mapped into a new value that is a function of all four bytes in that column. It is a substitution that makes use of arithmetic over GF(2^8). Each byte of a column is mapped into a new value that is a function of all four bytes in that column. It is designed as a matrix multiplication where each byte is treated as a polynomial in GF(28). The inverse used for decryption involves a different set of constants. The constants used are based on a linear code with maximal distance between code words – this gives good mixing of the bytes within each column. Combined with the “shift rows” step provides good avalanche, so that within a few rounds, all output bits depend on all input bits. Mix Columns The forward mix column transformation, called MixColumns Operates on each column individually Each byte of a column is mapped into a new value that is a function of all four bytes in that column It is a substitution that makes use of arithmetic over GF(28) The forward mix column transformation, called MixColumns, operates on each column individually. Each byte of a column is mapped into a new value that is a function of all four bytes in that column. It is a substitution . | Data Security and Encryption (CSE348) Lecture slides by Lawrie Brown for “Cryptography and Network Security”, 5/e, by William Stallings, briefly reviewing the text outline from Ch 0, and then presenting the content from Chapter 1 – “Introduction”. Lecture # 10 Review The AES selection process The details of Rijndael – the AES cipher looked at the steps in each round Out of four AES stages, two are discussed Substitute bytes Shift Rows Chapter 5 summary. Mix Columns Each column is processed separately Each byte is replaced by a value dependent on all 4 bytes in the column Effectively a matrix multiplication in GF(28) using prime poly m(x) =x8+x4+x3+x+1 The forward mix column transformation, called MixColumns, operates on each column individually. Each byte of a column is mapped into a new value that is a function of all four bytes in that column. It is a substitution that makes use of arithmetic over GF(2^8). Each byte of a column is mapped into a new .
