Modular Arithmetic and the RSA Cryptosystem

Nov 27, 2012

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Modular Arithmetic and the RSA Cryptosystem

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RSA cryptosystem--preview

RSA cryptosystem--preview. Suppose n=p q and  ( n )=( p -1)( q -1), where p and q are big primes. Select (find) a and b , such that a  b= 1 mod  ( n ). K =( n ,p,q,a, b ), publicize n , b , but keep p,q,a secret. For any x,y  Z n , define

378 views • 13 slides

RSA Cryptosystem

RSA Cryptosystem. by Drs. Charles Tappert and Ron Frank The information presented here comes primarily from https ://en.wikipedia.org/wiki/RSA_(cryptosystem ) and http://www.math.uchicago.edu/~ may/VIGRE/VIGRE2007/ REUPapers /FINALAPP/Calderbank.pdf. RSA Cryptosystem.

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RSA Asymmetric Key Cryptosystem

RSA Asymmetric Key Cryptosystem. Presented by Katherine Heller COSC 4765 University of Wyoming April 26, 2011. Asymmetric Key Cryptography. Introduced 1970’s Whitfield Diffie and Martin Hellman Known as Public Key Encryption (PKE) Eliminated need for shared private keys. RSA.

420 views • 19 slides

Modular Arithmetic and the RSA Cryptosystem

Modular Arithmetic and the RSA Cryptosystem. p-1. 1. ´ p. MAX(a,b) + MIN(a,b) = a+b. n|m means that m is a an integer multiple of n. We say that “n divides m”. True: 5|25 2|-66 7|35, False: 4|5 8|2. Greatest Common Divisor: GCD(x,y) = greatest k ¸ 1 s.t. k|x and k|y.

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Section 4.4: The RSA Cryptosystem

Section 4.4: The RSA Cryptosystem. Practice HW Handwritten and Maple Exercises p. 11-13 at end of class notes.

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The RSA Cryptosystem and Factoring Integers

The RSA Cryptosystem and Factoring Integers. OUTLINE. [1] Modular Arithmetic Algorithms [2] The RSA Cryptosystem [3] Quadratic Residues [4] Primality Testing [5] Square Roots Modulo n [6] Factoring [ 7] The Rabin Cryptosystem. [1] Modular Arithmetic Algorithms 1. The integers

637 views • 52 slides

Modular Arithmetic

Modular Arithmetic. Lecture 8. Modular Arithmetic. Def : a  b (mod n) iff n|( a - b) iff a mod n = b mod n. Modular Addition. Lemma : If a  c (mod n), and b  d (mod n) then a+b  c+d (mod n). Modular Multiplication.

945 views • 26 slides

RSA Cryptosystem

RSA Cryptosystem. What is RSA ?. RSA is a public-key cryptosystem . It was developed by Ronald Rivest, Adi Shamir, and Leonard Adleman in 1977. The security of the RSA system is based on the hard problem of factoring a large integer. Public-key cryptosystem.

619 views • 11 slides

The RSA Cryptosystem and Factoring Integers (I)

The RSA Cryptosystem and Factoring Integers (I). Rong-Jaye Chen. OUTLINE. [1] Modular Arithmetic Algorithms [2] The RSA Cryptosystem [3] Quadratic Residues [4] Primality Testing [5] Square Roots Modulo n [6] Factoring Algorithms [7] Other Attacks on RSA [ 8] The Rabin Cryptosystem

712 views • 46 slides

The RSA Cryptosystem and Factoring Integers (II)

The RSA Cryptosystem and Factoring Integers (II). Rong-Jaye Chen. OUTLINE. [1] Modular Arithmetic Algorithms [2] The RSA Cryptosystem [3] Quadratic Residues [4] Primality Testing [5] Square Roots Modulo n [6] Factoring Algorithms [7] Other Attacks on RSA [8] The Rabin Cryptosystem

486 views • 29 slides

RSA Cryptosystem

RSA Cryptosystem. Outline. Euler’s theorem ( §10.1.3) RSA cryptosystem ( §10.2.3) Definition Example Security Correctness Algorithms for RSA Modular power ( §10.1.4) Modular inverse ( §10.1.5) Randomized primality testing ( §10.1.6). Euler’s Theorem.

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The RSA Cryptosystem

The RSA Cryptosystem. Dan Boneh Stanford University. The RSA cryptosystem. First published: Scientific American, Aug. 1977. (after some censorship entanglements) Currently the “work horse” of Internet security: Most Public Key Infrastructure (PKI) products.

332 views • 20 slides

Modular Arithmetic and RSA Encryption

Modular Arithmetic and RSA Encryption. Stuart Reges Principal Lecturer University of Washington. Some basic terminology. Alice wants to send a secret message to Bob Eve is eavesdropping Cryptographers tell Alice and Bob how to encode their messages Cryptanalysts help Eve to break the code

117 views • 6 slides

Modular Arithmetic and the RSA Cryptosystem

Modular Arithmetic and the RSA Cryptosystem. p-1. 1.  p. Starring. Adleman. Shamir. Rivest. Euler. Fermat. The RSA Cryptosystem. R ivest, S hamir, and A delman (1978)

966 views • 92 slides

The RSA Cryptosystem and Factoring Integers

The RSA Cryptosystem and Factoring Integers. Rong-Jaye Chen. OUTLINE. [1] Modular Arithmetic Algorithms [2] The RSA Cryptosystem [3] Quadratic Residues [4] Primality Testing [5] Square Roots Modulo n [6] Factoring [ 7] The Rabin Cryptosystem. [1] Modular Arithmetic Algorithms

540 views • 52 slides

Modular Arithmetic and the RSA Cryptosystem

Modular Arithmetic and the RSA Cryptosystem. p-1. 1. ´ p. MAX(a,b) + MIN(a,b) = a+b. n|m means that m is an integer multiple of n. We say that “n divides m”. True: 5|25 2|-66 7|35, False: 4|5 8|2. Greatest Common Divisor: GCD(x,y) = greatest k ¸ 1 s.t. k|x and k|y.

984 views • 97 slides

The RSA Cryptosystem and Factoring Integers (II)

304 views • 29 slides

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