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EPFL-IC-IIF-LACAL Marcelo E. Kaihara April 27 th , 2007

Algorithms for public-key cryptology Montgomery Arithmetic. EPFL-IC-IIF-LACAL Marcelo E. Kaihara April 27 th , 2007. Motivation. RSA:. ElGamal:. Most of the time computing modular multiplications. Need of efficient algorithms for modular multiplication . Notation.

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CS433: Computer System Organization

CS433: Computer System Organization. Main Memory Virtual Memory Translation Lookaside Buffer. Acknowledgement. Slides from previous CS433 semesters TLB figures taken from http://www.cs.binghamton.edu/~kang/cs350/Chapter08.ppt

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CSE 311 Foundations of Computing I

CSE 311 Foundations of Computing I. Lecture 12 Primes, GCD, Modular Inverse Spring 2013. Announcements. Reading assignments Today : 7 th Edition: 4.3-4.4 (the rest of the chapter is interesting!) 6 th Edition: 3.5, 3.6 Monday: Mathematical Induction 7 th Edition: 5.1, 5.2

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CSE 311 Foundations of Computing I

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Cryptography and Network Security

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Lecture 6

Lecture 6 Hashing Motivating Example Want to store a list whose elements are integers between 1 and 5 Will define an array of size 5, and if the list has element j, then j is stored in A[j-1], otherwise A[j-1] contains 0. Complexity of find operation is O(1) Hash table

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Classical Cryptography

Classical Cryptography. The Enigma Rotor machine. The Jefferson cylinder. Scytale. Hieroglyphics. Symmetric Cryptography. Uses a single key for both encryption and decryption The encryption and decryption algorithms are inverses of each other.

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321 Section, 2-7

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Discrete Mathematics CS 2610

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Modular Arithmetic

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Congruences (2/17)

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Prime Numbers (3/17 )

Prime Numbers (3/17 ). We all know what a prime number is. Theorem (Euclid). There are infinitely many primes.

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