7. Cryptography: asymmetric encryption Flashcards
What is a generator?
If p is prime, g is a generator and x is any integer g^x mod p is equally likely to be any number between 0 and p-1
What does Z_p (integers subscript p) mean?
integers mod p, i.e 0 … p - 1
What does TTP stand for?
Online Trusted Third Party
How does TTP work?
What are the components of a public-key encryption algorithm?
What is the Euler function?
What is phi(p) where phi is the Euler function and p is a prime number?
p - 1
What is phi(pq) where phi is the Euler function and p, q are prime numbers?
(p - 1)(q - 1)
What is Z_n star (Z subscript n superscript star)
What is eulers theorem?
What are the 4 intractable problems (for this course)?
- Factoring
- RSAP
- Discrete Log
- DHP
What is the factoring problem?
What is the RSAP problem?
What is the discrete log problem?
What is the DHP problem?
What is the public key for ElGamel?
g^d (mod p)
Where p is a prime, g is a generator for p and d is random between 1 and p - 2
What is the private key for ElGamel?
d
Where d is a random value between 1 and p - 2
How do you encrypt with ElGamel?
E(pk, m) = (g^r mod p, m * (g^d) ^r mod p)
Where r is a random integer, g^d mod p is the public key and m is the message
How do you decrypt with ElGamel?
D(sk, x) = e^-d * c
Where x is the cipher text, x = (e, c) and d is the secret key
Show the ElGamel is consistent
Note that x should be m
