Cryptosystem
Substitution cipher
Shift cipher
The shift cipher is a special case of the substitution cipher. Instead of forming any permutation we allow only those that shift the alphabet by a specific offset. The offset is the key 0 ≤ k ≤ 25.
Vigenère cipher
Permutation cipher
For a cryptosystem we need:
- to be able to efficiently compute the encryption and decryption functions
- that an unauthorised party should not be able to determine the key or the plaintext
Brute force attack
An exhaustive search of a keyspace involves trying all possible decryption keys.
Kerckhoffs’ desiderata
- The system should be, if not theoretically unbreakable, unbreakable in practice.
- Compromise of the system details should not inconvenience the correspondents.
- The key should be rememberable without notes and easily changed.
- The cryptogram should be transmissible by telegraphy.
- The encryption apparatus should be portable and operable by a single person.
- The system should be easy, requiring neither the knowledge of a long list of rules nor mental strain
Kerckhoffs’ principle
Compromise of the system details should not inconvenience the correspondents.
Cipher text only attack
Known plain text attack
Chosen plain text attack
Chosen cipher text attack
Computationally secure
A cryptosystem is computationally secure if the best algorithm for breaking it requires a computational effort which is greater than the computational resources of the assumed attacker.
- We need a measure of the computational effort to break the cryptosystem.
- We can’t prove a system is computationally secure against all attacks
Provable security
If the cryptosystem can be broken then we can efficiently solve problem A, where problem A is
- Well studied
- Thought to be “difficult”
This is not an absolute proof of security but a proof of the security relative to another problem.
Unconditionally secure
A cryptosystem is said to be unconditionally secure if an attacker with infinite computational resources cannot break the system.
Vernam cipher
Vernam cipher as one-time pad
An unconditionally secure cryptosystem
