Lecture 1 Flashcards
1
Q
How is a positive integer denoted?
A
N
2
Q
How is a prime denoted?
A
p
3
Q
What is Zn?
A
The set of integers (0, 1, …, N-1}
4
Q
How do we return to the correct range of Zn values?
A
Add or subtract k.N to get back into the range.
5
Q
What is Zm?
A
Modulus which is:
- An abelian group, which means all modular arithmetic will give security in consistent results.
- A ring, meaning these operations will be well-behaved, always working correctly and maintaining the mathematical structure and environment.
6
Q
What is Bezout’s identity?
A
For all non-zero x, y in Z, there exists a,b in Z such that
ax + by = gcd(x, y)
GCD = greatest common divisor
7
Q
What is an efficient algorithm to find GCDs?
A
Extended Euclidian Algorithm
8
Q
How can GCDs be found with Sage?
A
do this
9
Q
A
