Deck 2: Introduction to Number Theory

Question 1

For many cryptographic algorithms, it is necessary to select one or more very large prime numbers.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

the algorithm credited to Euclid for easily finding the greatest
common divisor of two integers has broad significance in cryptography.

Answer 3

True

Question 4

Unlike ordinary addition, there is not an additive inverse to each
integer in modular arithmetic.

Question 5

If b|a we say that b is a divisor of A.

Question 6

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

Question 7

the scheme where you can find the greatest common divisor of
two integers by repetitive application of the division algorithm is
known as the Brady algorithm.

Question 8

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

Question 9

All integers have primitive roots.

Question 10

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

Question 11

two integers a and b are said to be congruent modulo n, if
(a mod n) = (b mod n).

Question 12

Basic concepts from number theory that are needed for understanding finite fields include divisibility, the Euclidian algorithm, and modular arithmetic.

Question 13

the rules for ordinary arithmetic involving addition, subtraction,
and multiplication carry over into modular arithmetic.
9.two theorems that play important roles in public-key cryptography are Fermat's theorem and Euler's theorem.