Exam 8: More Number Theory

The mapping of the CRT equation is a one-to-one correspondence called a _________ between Zm and the Cartesian product Zm1 X Zm2 X ...X Zmk.

The _________ of a number is defined to be the power to which some positive base except 1)must be raised in order to equal the number.

An integer p > 1 is a __________ number if and only if its only divisors are + 1 and + 1.

Prime numbers play a very small role in cryptography.

A prime number can have a remainder when divided by positive or negative values of itself.

The number 37 is prime so therefore all of the positive integers from 1 to 36 are relatively prime to 37.

One of the useful features of the Chinese remainder theorem is that it provides a way to manipulate potentially very large numbers mod M in terms of tuples of smaller numbers.

The primitive roots for the prime number 19 are 2,3,10,13,14 and 15.

Discrete logarithms are fundamental to the digital signature algorithm and the _________ algorithm.

If p is prime and a is a positive integer,then ap = amod p)is an alternative form of _________ theorem.

The first assertion of the CRT,concerning arithmetic operations, follows from the rules for modular arithmetic.

A __________ number is an integer that can only be divided by positive and negative values of itself and 1 without having a remainder.

Miller's test will return __________ if it fails to detect that n is not prime.

The logarithm of a number is defined to be the power to which some positive base except 1)must be raised in order to equal the number.

Two numbers are relatively prime if their greatest common divisor is _________ .

All integers have primitive roots.

With ordinary positive real numbers the logarithm function is the inverse of exponentiation.

Discrete logarithms are not fundamental to public-key algorithms.

The Miller-Rabin test can determine if a number is not prime but cannot determine if a number is prime.

The _________ algorithm is typically used to test a large number for primality.