How can geometry be useful for Cryptography Elliptic curves can be defined in a finite or galois field gF y2=x3+ ax+ b mod p where the field size p is a prime number and 10, 1. p-1 is an abelian group under addition mod p and 1. p-1 is an abelian group under multiplication mod p25 How can Geometry be useful for Cryptography? Elliptic curves can be defined in a finite or Galois field GFp : y 2 = x 3 + ax + b mod p where the field size p is a prime number and {0,1, ..., p-1} is an abelian group under addition mod p and {1, ..., p-1} is an abelian group under multiplication mod p