Mohak_Bheda_HW5.docx - Homework 5 ECE/CS 5560 MOHAK BHEDA Chapter 10 Problem 10.7 Solution 2Q = Also called the point at infinity and designated by O

# Mohak_Bheda_HW5.docx - Homework 5 ECE/CS 5560 MOHAK BHEDA...

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Homework 5 ECE/CS 5560 MOHAK BHEDA Chapter 10 Problem 10.7 Solution: 2Q = Also called the point at infinity and designated by O. This value serves as the additive identity in elliptic-curve arithmetic. Hence, 2Q =0 3Q = 2Q + Q = 0 + Q = Q Problem 10.11 Solution: 4(a^3) + 27(b^2) mod 7 = 112 mod 7 = 0 This elliptic curve does not satisfy the condition and therefore does not define a group over Z 7 . Problem 10.12

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Solution: E 7 (2,1). y^2 = x^3 + 2x + 1, p = 7. x (x^3 + 2x + 1) mod 7 Square root mod 7 exists ? y 0 1 yes 1,6 1 4 yes 2,5 2 6 no 3 6 no 4 3 no 5 3 no 6 5 no Problem 10.16 Solution: a) RHS = S + K Y A = M K Y A G + K Y A G after substituting the values of S and Y A RHS = M = LHS b) The imposter gets Alice’s public verifying key Y A and sends Bob M, k, and S = M – Y A for any k. Chapter 14
Problem 14.4 Solution: Attached are the certificates obtained from my system. Trusted Root Certificate Intermediate certificate

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Problem 14.6 Solution:
a) A believes that she shares K AB ' with B since the response that A received was encrypted by a key known only to A and B and it also contained N A , that was transmitted by A to B. B believes that he shares K AB ' with A since the response that B received after encrypting [ N A , K AB ' ] contained N A encrypted by K AB ' , which he had sent to A only. A believes that K AB ' is fresh since it sends a nonce N A to B, thus it can validate the existence and it being fresh.

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• Fall '14
• JungMinPark
• Cryptography, Public-key cryptography, Certificate authority, bob M

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