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COSC 4P03 Week 91 Public Key Cryptography Slides courtesy of Professor Sheridan Houghten

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COSC 4P03 Week 92 Public Key Cryptography – History For many years, the idea was attributed to Diffie and Hellman, who presented the idea at a conference in 1976 and published the idea the same year A recent report indicates the idea was first proposed by J.H.Ellis at CESG in the UK in 1970, but classified as “top secret” The scheme now known as RSA (named for Rivest, Shamir & Adleman who “invented” it in 1977) was first proposed by C.Cocks in a CESG report in 1973

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COSC 4P03 Week 93 Multiplicative Inverse – Algorithm 5.3 MultiplicativeInverse(a,b)// Find b -1 mod a { a0 = a; b0 = b; t0 = 0; t = 1; q = floor(a0/b0);// quotient r = a0 – q * b0;// remainder while(r > 0) { temp = (t0 – q * t) mod a; t0 = t; t = temp; a0 = b0; b0 = r; q = floor(a0/b0); r = a0 – q * b0; } if (b0 != 1) b has no inverse mod a else b -1 = t; }

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COSC 4P03 Week 94 Multiplicative Inverse Example – find inverse of 28 mod 75 Iterationtempa0b0t0tqr Start

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COSC 4P03 Week 95 Square and Multiply – Algorithm 5.5 SquareAndMultiply(x,c,n) { z = 1; for(i = l-1; i >= 0; i--) { z = z*z mod n; if(c[i] == 1) z = z*x mod n; }

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COSC 4P03 Week 96 Square and Multiply Example n = and b = 3533 (binary: (so l = 12)) Plaintext: 9726 ib[i]z * 9726 mod = * 9726 mod = mod = * 9726 mod = * 9726 mod = * 9726 mod = mod = mod = * 9726 mod = * 9726 mod = mod = * 9726 mod = 5761

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