Transcription of MATHEMATICAL CRYPTOLOGY - TUT
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MATHEMATICAL CRYPTOLOGY - TUT
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 ALGEBRA: Curves85X ELGAMAL.
Though the union of mathematics and cryptology is old, it really came to the fore in con- nection with the powerful encrypting methods used during the Second World War and their subsequent breaking.
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