MATH 115: ELEMENTARY NUMBER THEORY HOMEWORK # 3

JOHN VOIGHT

This homework is not due! It is just for fun. Homework #8 (Freebie):

• §13.1: 1, 2, 8

• Elliptic Curves: EC1: Let E : y^{2} = x^{3} − x + 1 over ℤ/3ℤ.

(a) Determine #E(ℤ/3ℤ).

(b) Alice and Bob do a Diffie-Hellman key exchange using the group E(ℤ/3ℤ), where E : y^{2} = x^{3} − x + 1, with g = (1, 1). They use secret exponents a = 2 and b = 3. What is the secret common key that they exchange?