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+# CSE4303 Introduction to Computer Security (Lecture 5)
+
+## Cryptography: Foundations
+
+### Definitions
+
+Cryptography is the study of techniques that enable secure communication and computation in the presence of adversaries, by providing formal guarantees such as confidentiality, integrity, and authenticity.
+
+Cryptanalysis is the study of techniques for breaking cryptographic systems, by recovering secret information or violating security guarantees without knowing the secret key
+
+### Background: security guarantee
+
+- Well-defined statement about difficulty of compromising a system
+  - ...with clear implicit or explicit assumptions about:
+    - Parameters of the system
+    - Threat model
+    - Attack surfaces
+- Example: "A one-time pad cipher is secure against any cryptanalysis, including a brute-force attack, assuming:
+  - the key is the same length as the plaintext,
+  - the key is truly random, and
+  - the key is never re-used.
+- Example: "Given that keys remain uncompromised (by human error, side channel, etc.), recovering an RSA private key from a given public key is at least as hard as integer factorization."
+  - I.e. we can reduce RSA to integer factorization.
+  - Note: correct implementation is not guaranteed!
+- Non-example: "This app is secure."
+  - Empty claim: what does it mean?
+
+### Overview: Encryption and Decryption
+
+- The message m is called the plaintext.
+- Alice will convert plaintext m to an encrypted form using an encryption algorithm E that outputs a ciphertext c for m
+
+#### Cryptography goals
+
+- Confidentiality:
+  - Mallory and Eve cannot recover original message from ciphertext
+- Integrity:
+  - Mallory cannot modify message from Alice to Bob without detection
+by Bob
+- Authenticity:
+  - Mallory cannot craft a message that Bob would accept as coming from Alice
+
+#### Cryptosystem compoents
+
+1. The set of possible plaintexts (M)
+2. The set of possible ciphertexts (C)
+3. The set of encryption keys (K)
+4. The set of decryption keys (usually K as well)
+5. The correspondence between encryption keys and decryption
+keys
+6. The encryption algorithm to use (E)
+7. The decryption algorithm to use (D)
+
+#### Symmetric ciphers:
+
+A cipher defined over $(K,M,C)$ is a pair of efficient algorithms $(E,D)$ where $E: K\times M\to C$ and $D: K\times C \to M$
+
+Correctness Property:
+
+$\forall m\in M, \exists k\in K$, $E(k,m) = c\in C$, and $D(k,c) = m$
+
+- $D$ and $E$ are often efficient (polynomial time | concrete time)
+- $E$ is encryption, often randomized.
+- $D$ is decryption, always deterministic.
+
+#### Threat models
+
+Attackers may have:
+
+- collection of ciphertexts (ciphertext-only attack)
+- collection of plaintext/ciphertext pairs (known plaintext attack: KPA )
+- collection of plaintext/ciphertext pairs for plaintexts selected by the attacker (chosen plaintext attack: CPA )
+- collection of plaintext/ciphertext pairs for ciphertexts selected by the attacker (chosen ciphertext attack: CCA/CCA2 )
+
+### Symmetric (shared-key) encryption
+
+Refer to this lecture notes
+
+[CSE442T Lecture 1](https://notenextra.trance-0.com/CSE442T/CSE442T_L1/)
+