IAS FINAL EXAM 7-12

Prime numbers play a very small role in cryptography.

• F

• T

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.

• T

• F

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

• T

• F

All integers have primitive roots.

• T

• F

An area of ongoing research is the development of efficient algorithms for determining if a randomly chosen large integer is a prime number.

• T

• F

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

• F

• T

Discrete logarithms are not fundamental to public-key algorithms.

• F

• T

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

• T

• F

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

• T

• F

The Chinese Remainder Theorem is believed to have been discovered by the Chinese mathematician Agrawal in 100 A.D.

• F

• T