Transcription of MATHEMATICAL CRYPTOLOGY - TUT
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MATHEMATICAL CRYPTOLOGYK eijo Ruohonen(Translation by Jussi Kangas and Paul Coughlan)2014 Contents1I INTRODUCTION3II NUMBER THEORY: PART , Factors, of Integers in Different Common Divisor and Least Common Calculus or Modular Class Rings and Prime Arithmetic Operations for Large Integers14 Addition and subtraction14 Multiplication16 Division18 Powers19 Integral root21 Generating a random integer23 III SOME CLASSICAL CRYPTOSYSTEMS PERMUTATION. AFFINE-HILL. VIGEN ALGEBRA: RINGS AND and Fields34V Bytes (SubBytes) Rows (ShiftRows) Columns (MixColumns) Round Keys (AddRoundKey) the Variant of s Modes of AESiii42VI PUBLIC-KEY Theory of and Fall of Knapsack Suitable for Public-Key Encryption48 VII NUMBER THEORY: PART s Function and Euler s and Discrete Remainder and Generating of Square Random LLL Algorithm65 VIII and and Partial Information about by LLL Algorithm74IX
iv —mostly certain fields of number theory and algebra—has been remarkably fast. It is no exag-geration to say that the recent popularity of number theory and algebra is expressly because of
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