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(3) Let the elliptic curve & be y² = x³ + x + 6 (mod 11). (a) Given the point a = (2, 7) on the elliptic curve E, calculate 2a and 3a. (b) Consider the elliptic curve ElGamal cryptosystem. Let the private key be s = 7. (i) What is the public key? (Hint: You don't need to include the known information E, p, a in the public key, but have to calculate = sa. ) (ii) Encoding: Suppose the text has been converted to a point x = (10, 9) on E. Choose the random number k = 3. What are the points (or numbers) to be transmitted? (iii) Decoding: When receiving information from (ii), how to recover the original text?

(3) Let the elliptic curve & be y² = x³ + x + 6 (mod 11). (a) Given the point a = (2, 7) on the elliptic curve E, calculate 2a and 3a. (b) Consider the elliptic curve ElGamal cryptosystem. Let the private key be s = 7. (i) What is the public key? (Hint: You don't need to include the known information E, p, a in the public key, but have to calculate = sa. ) (ii) Encoding: Suppose the text has been converted to a point x = (10, 9) on E. Choose the random number k = 3. What are the points (or numbers) to be transmitted? (iii) Decoding: When receiving information from (ii), how to recover the original text?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(3) Let the elliptic curve & be y² = x³ + x + 6 (mod 11). (a) Given the point a = (2,7) on the elliptic curve E, calculate 2a and 3a. (b) Consider the elliptic curve ElGamal cryptosystem. Let the private key be s = 7. (i) What is the public key? (Hint: You don't need to include the known information E, p, a in the public key, but have to calculate = sa. ) (ii) Encoding: Suppose the text has been converted to a point x = (10, 9) on E. Choose the random number k 3. What are the points (or numbers) to be transmitted? = (iii) Decoding: When receiving information from (ii), how to recover the original text?
Transcribed Image Text:(3) Let the elliptic curve & be y² = x³ + x + 6 (mod 11). (a) Given the point a = (2,7) on the elliptic curve E, calculate 2a and 3a. (b) Consider the elliptic curve ElGamal cryptosystem. Let the private key be s = 7. (i) What is the public key? (Hint: You don't need to include the known information E, p, a in the public key, but have to calculate = sa. ) (ii) Encoding: Suppose the text has been converted to a point x = (10, 9) on E. Choose the random number k 3. What are the points (or numbers) to be transmitted? = (iii) Decoding: When receiving information from (ii), how to recover the original text?
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