1. 2. Perfect Secret Encryption
CIS Cryptography
2. Perfect Secret Encryption

2. Encryption Plaintext Ciphertext Encryption Decryption encryption key
decryption key
Encryption
Plaintext
Ciphertext
Decryption

3. Encryption schemes

4. Encryption schemes Definition
An encryption scheme (Gen,Enc,Dec) over message space M is perfectly secret if for every probability distribution over M, every message mM, and every ciphertext cC for which Pr[C = c]  0:
Pr[M = m | C = c] = Pr[M = m]
Convention:
We consider only probability distributions over M, C that assign non-zero probabilities to all mM and cC.

5. Encryption schemes Lemma 1
An encryption scheme (Gen,Enc,Dec) over message space M is perfectly secret if and only if for every probability distribution over M, every message mM, and every ciphertext cC:
Pr[C = c | M = m] = Pr[C = c]

6. Encryption schemes

7. Encryption schemes
An equivalent definition for perfect secrecy

8. Encryption schemes

9. Shannon’s Theorem Theorem
Let (Gen,Enc,Dec) be an encryption scheme over a message space M for which |M|= |K|=|C|. The scheme is perfectly secret if and only if:
Every key kK is chosen with equal probability 1/|K| by algorithm Gen.
For every mM and every cC there is a unique key kK such that Enck(m) outputs c

10. Encryption algorithms

11. Encryption schemes Theorem
The one time pad encryption scheme is perfectly secret.

12. Limitations to perfect secrecy
Theorem
Let (Gen,Enc,Dec) be a perfectly secret encryption scheme over message space M, and let K be the key space as determined by Gen.
Then |K|  |M| .