Lecture-6-7-Crtpto-2-1-3-10

Lecture-6-7-Crtpto-2-1-3-10 - Modular Arithmetic...

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Modular Arithmetic Cryptographic Techniques Ratan Guha CIS 3360 Security in Computing Spring 2010 2-1 and 2-3-10 Lecture 6 and 7 1
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2 Resources Used Cryptography and Network Security, Fourth Edition, by William Stallings Lecture slides for the textbook by Lawrie Brown Lecture slides by Henric Johnson,Blekinge Institute of Technology, Sweden
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3 Outline Outline Reading Assignment: Chapter 2 Modular Arithmetic Some Basic Terminology Conventional Encryption Principles Characteristics of Cryptographic Techniques Symmetric Encryption Some Classical Symmetric Encryption Algorithms Modern Symmetric Encryption Techniques
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Modular Arithmetic define modulo operator a mod n” to be remainder when a is divided by n use the term congruence for: a = b mod n when divided by n, a & b have same remainder eg. 100 = 34 mod 11 b is called a residue of a mod n since with integers can always write: a = qn + b usually chose smallest positive remainder as residue ie. 0 <= b <= n-1 process is known as modulo reduction eg. -12 mod 7 = -5 mod 7 = 2 mod 7 = 9 mod 7
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Modular Arithmetic Operations is 'clock arithmetic' uses a finite number of values, and loops back from either end modular arithmetic is when do addition & multiplication and modulo reduce answer can do reduction at any point, ie a+b mod n = [a mod n + b mod n] mod n a * b mod n = [a mod n * b mod n] mod n
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6 Some Basic Terminology plaintext - original message ciphertext - coded message cipher - algorithm for transforming plaintext to ciphertext key - info used in cipher known only to sender/receiver encipher (encrypt) - converting plaintext to ciphertext decipher (decrypt) - recovering ciphertext from plaintext cryptography - study of encryption principles/methods cryptanalysis (codebreaking) - study of principles/ methods of deciphering ciphertext without knowing key cryptology - field of both cryptography and cryptanalysis
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7 Conventional Encryption Conventional Encryption Principles Principles
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Lecture-6-7-Crtpto-2-1-3-10 - Modular Arithmetic...

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