# Cryptography Flashcards

1
Q

Caesar cipher

A

Encrypt with x + 3
Decrypt with x - 3

2
Q

Vigenere cipher

A

Given vector responding to keyword eg. ABC is 123
Then
Hello = 8,5,11,11,14
Goes to
8+1, 5+2, 11+3, 11+1, 14+2
9,7,14,12,16

3
Q

In RSA one chooses

A
• 2 large primes p != q to form n=pq
• 2<=e<=φ(n) such that gcd(e, φ(n)) = 1
-compute 2<=s<=φ(n) such that es = 1 mod(φ(n))

e is encryption s is decryption

4
Q

Public key in RSA

A

kp = (n,e)

5
Q

RSA secret key

A

Ks = (n,s)

6
Q

RSA encryption function

A
7
Q

RSA decryption function

A
8
Q

RSA plaintext and cipher text alphabets

A
9
Q

RSA key space

A
10
Q

Prove

A
11
Q

To send plaintext, RSA

A

-Compute c = me mod(n)
Where m is message

12
Q

To decipher c, RSA

A

Compute (by FLT and Euler’s Theorem)

13
Q

Quick way to calculate φ(n) for RSA

A

Φ(n) = (p-1)(q-1) where pq=n (primes p!=q)

14
Q

Basic principle

A
15
Q

Proof of basic principle

A
16
Q

Fermats primality test

A
17
Q

Carmichael’s numbers

A
18
Q

What implies that n is squarefree?

A

Implies n is squarefree

19
Q

Let n>1 be an odd integer. n-1=2k * u (for odd u), then?

A

-n is prime <=>

20
Q

Miller Rabin primality test

A
21
Q

Miller Rabin witness to the compositness of n

A
22
Q

Theorem that states that Miller Rabin test has a very high probability of deciding wether a given integer is composite

A
23
Q

To compute p and q from n = pq and φ(n)

A