crypto hw

crypto hw - Zhou, HuanXian ID: 0225418 CS393 Crypto HW...

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Unformatted text preview: Zhou, HuanXian ID: 0225418 CS393 Crypto HW PROBLEM #1 Using the prime numbers p=13 q=3 Compute an RSA public and private key pair of (n,e) and (n,d) respectively. Using the last two digits of your Poly student ID, XY calculate XYmod38 as the message m. So for example if the last two digits of your Poly ID are 99 then 99mod38=23 and you would use 23 as the message m. Verify decryption using the private key (n,d) Show all steps in the computation. Be verbose. When calculating large exponents in a modulus be sure to use the binary expansion technique. Show all steps of this binary expansion. n = p∙q = 13*3 =39 Φ(n) = 12*2 =24 Choose e = 7, relatively prime to 24 d = e- 1 mod Φ = 7- 1 mod 24 = ( * + )/ Φ y 1 e where y = 1,2,3,4 …. = (24*y + 1)/7 = 31 when y = 9 Public key: (39,7) Private key: (39,31) M = 18 mod 38 = 18 Y = E(m) = me mod n = 187 mod 39 = + + 184 2 1 mod 39 = ( 184 ∙ 182 ∙ ) 181 mod 39 = 181 mod 39 18 = 182 mod 39 12 = 184 mod 39 27 = ( ) 27∙12∙18 mod 39...
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This note was uploaded on 11/02/2010 for the course CS 393 taught by Professor Staff during the Spring '08 term at NYU Poly.

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crypto hw - Zhou, HuanXian ID: 0225418 CS393 Crypto HW...

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