Exam 8: More Number Theory

For any integer b and a primitive root a of prime number p we can find a unique exponent i .This exponent i is referred to as the ___________ .

Discrete logarithms are analogous to ordinary logarithms but are defined using __________ arithmetic.

The procedure TEST takes a candidate integer n as input and returns the result __________ if n is definitely not a prime.

The number of positive integers less than n and relatively prime to n is referred to as __________ function.

Discrete logarithms are fundamental to a number of public-key algorithms including __________ key exchange and the DSA.

Two numbers are relatively prime if they have _________ prime factors in common.

Two theorems that play important roles in public-key cryptography are Fermat's theorem and __________ theorem.

A one-to-one correspondence is called __________ .

A _________ number can only be divided by +/- values of itself and 1 and cannot have a remainder.

Although it does not appear to be as efficient as the Miller-Rabin algorithm,in 2002 a relatively simple deterministic algorithm that efficiently determines whether a given large number is a prime was developed.This algorithm is known as the _________ algorithm.

An important requirement in a number of cryptographic algorithms is the ability to choose a large prime number.

Two numbers are relatively prime if they have ________ prime factors in common.

Discrete logarithms are analogous to ordinary logarithms but are defined using modular arithmetic.

Two numbers are __________ if their greatest common divisor is 1.

The __________ theorem states that it is possible to reconstruct integers in a certain range from their residues modulo a set of pairwise relatively prime moduli.

If a number is the highest possible exponent to which a number can belong,it is referred to as a _________ of n.

__________ theorem states the following: If p is prime and a is a positive integer not divisible by p,then ap-1 = 1mod p).

Discrete logarithms are fundamental to the ____________ .

Prime numbers play a _________ role in number theory.

An important quantity in number theory referred to as __________ ,is defined as the number of positive integers less than n and relatively prime to n.