Basic concepts¶
Symmetric-key encryption scheme(SKES)¶
Definition: Symmetric-key encryption scheme(SKES)
Consist of:
- Spaces:
- \(M\), plaintext space
- \(C\), ciphertext space
- \(K\), key space.
- Functions:
- Encryption functions: \(E_k: M \to C, \forall k \in K\)
- Decryption functions: \(D_k: C \to M, \forall k \in K\)
- Satisfy that: \(D_k(E_k(m)) = m, \forall m \in M, k \in K\)
How to ensure confidentiality:
- Alice & Bob agree on a secret key \(k\) through a "secure channel"
- Alice compute \(c = E_k(m)\) and send \(c\) to Bob through a "unsecure channel".
- Bob receive \(c\) and compute \(m = D_k(c)\) to get plaintext \(m\).
Security & Attack method¶
Basic assumption: adversary knows everything, except the key \(k\)
Perspective of Adversary's Goal¶
If the adversary can get:
| key | plaintext | partial information | |
|---|---|---|---|
| Totally Insecure | maybe | yes | -- |
| Semantic insecure | no | no | yes |
Perspective of Adversary's Interation¶
- Passive attack
- ciphertext-only
- known-plaintext: know some of the plaintext and corresponding ciphertext
- Active attack:
- chosen-plaintext: choose some plaintext and get corresponding ciphertext
- chosen-ciphertext: choose some ciphertext and get corresponding plaintext.
- Notice: stronger than chosen-plaintext.
- Other attack:
- Side channel attack
- Physical attacks
Perspective of Adversary's power¶
- Information-theoretic security: Eve has infinite computational resources
- Complexity-theoretic security: Eve has a polynomial-time Turing machine. (super polynomial)
- Computational security: Eve is bounded by real world computers.
\(2^{40}\) -- easy, \(2^{64}\) -- feasible, \(2^{128}\) nearly impossible.
Definition of Secure¶
By three perspectives:
- Interaction: Chosen-plaintext Attack
- Power: computationally bounded
- Goal: Semantically secure(no any partial information exclude length)
Break insecure ones:
- ciphertext c
- can query plaintext, get corresponding ciphertext
- do feasible computation
- get the message \(m\) or any partial information
Security Level \(l\): * \(2^l\) operations to attack on the scheme