Consider the elliptic curve group based on the equation y = x + ax+b mod p...

Transcribed Image Text:

Consider the elliptic curve group based on the equation y² = x³ + ax+b mod p where a = 952, b = 873, and p = 2063. We will use these values as the parameters for a session of Elliptic Curve Diffie-Hellman Key Exchange. We will use P = (1,324) as a subgroup generator. You may want to use mathematical software to help with the computations, such as the Sage Cell Server (SCS). On the SCS you can construct this group as: G=Elliptic Curve(GF(2063),[952,873]) Here is a working example. (Note that the output on SCS is in the form of homogeneous coordinates. If you do not care about the details simply ignore the 3rd coordinate of output.) Alice selects the private key 31 and Bob selects the private key 19. What is A, the public key of Alice? What is B, the public key of Bob? After exchanging public keys, Alice and Bob both derive the same secret elliptic curve point TAB- The shared secret will be the a-coordinate of TAB. What is it? Consider the elliptic curve group based on the equation y² = x³ + ax+b mod p where a = 952, b = 873, and p = 2063. We will use these values as the parameters for a session of Elliptic Curve Diffie-Hellman Key Exchange. We will use P = (1,324) as a subgroup generator. You may want to use mathematical software to help with the computations, such as the Sage Cell Server (SCS). On the SCS you can construct this group as: G=Elliptic Curve(GF(2063),[952,873]) Here is a working example. (Note that the output on SCS is in the form of homogeneous coordinates. If you do not care about the details simply ignore the 3rd coordinate of output.) Alice selects the private key 31 and Bob selects the private key 19. What is A, the public key of Alice? What is B, the public key of Bob? After exchanging public keys, Alice and Bob both derive the same secret elliptic curve point TAB- The shared secret will be the a-coordinate of TAB. What is it?

Answer rating: 100% (QA)

ANSWER dubion Public Key A Private key A V generator 2958 x 0236 69808 QA 7 ... View the full answer