Formulae

Question 1

How to initialize an RSA ?

Answer 1

— choose p, q prime numbers
— compute n = p×q and z = (p-1)×(q-1)
— choose an integer e such that 1<e<z and e, z share no other divisor than 1
— find d such that e×d - 1 mod z = 0

Question 2

xy mod p = ?
(Useful modulo trick)

Answer 2

xy mod p = [(x mod p)(y mod p)] mod p

Question 3

Outline the parameters of Diffie-Hellman

Answer 3

Xa, Xb = private keys
Ya, Yb = public keys
Kab = shared secret key

Question 4

How to initialize a Diffie-Hellman (starting from alpha, q) ?

Answer 4

Each peer chooses their private key (Xa, Xb)
Ya = alpha^Xa mod q
Yb = alpha^Xb mod q
Kab = alpha^Xa×Xb mod q = Ya^Xb mod q = Yb^Xa mod q

Question 5

How to define and use a Hill cipher ?

Answer 5

Define K, square matrix n × n
q prime number
P = message, or a chunk of the message of length n
C = K × P mod q (as many times as needed to cover all the chunks of the original message)

Question 6

How to cipher using RSA ?

Answer 6

C = M^e mod n

Question 7

How to decipher using RSA ?

Answer 7

M = C^d mod n