Foundations

1. Foundations The problem of providing secret communication over insecure media is the most traditional and basic problem of cryptography.

2. ◎Foundations Terminology: Sender vs. Receiver Messages vs. Encryption Encryption vs. Decryption Algorithms vs. Ciphers Symmetric alg. vs. Public-Key alg. Cryptanalysis Security of Cryptosystems Classical Cryptography vs. PKC Plaintext Plaintext Original Encryption Ciphertext Decryption Plaintext A cryptographic algorithm, also called a cipher, is the mathematical function used for encryption and decryption. To encrypt a plaintext message, apply an encryption algorithm to the plaintext. To decrypt a ciphertext , apply a decryption algorithm to the ciphertext.

3. ◎Foundations E(P) = C D(C) = P , D( E(P) ) = P ; describe these terms P, C, E, D ? If the security of an algorithm is based on keeping the nature of the algorithm secret, it is called RESTRICTED(algorithm). There are two general forms of key-based algorithms: symmetric and public-key. Symmetric algorithms are algorithms where the encryption key can be calculated from the decryption key and vice versa. In many such systems, the encryption key and the decryption key are the same. VS.

4. ◎Foundations PS. Symmetric algorithm are also called secret-key alg, single-key alg. or one-key alg.. Symmetric algotithms can also be divided into two categories: (a) stream algorithms or stream ciphers (b) block algorithms or block ciphers KEY Plaintext Original Encryption Ciphertext Decryption Plaintext Encryption KEY (public key) Decryption KEY (private key) Plaintext Original Encryption Ciphertext Decryption Plaintext

5. ◎Foundations In this class, ALGORITHM will refer specifically to the MATHEMATICAL TRANSFORMATIONS for encryption and decryption. CRYPTOSYSTEMS will refer to the algorithm, plus the way in which it is implemented. There are three kinds of cryptographic functions: hash functions, secret key functions, and public key functions. We will describe what each kind is, and what it is useful for. Public key cryptography involves the use of two keys. Secret key cryptography involves the use of one key. Hash functions involve the use of zero keys ! Try to imagine what that could possibly mean, and what use it could possibly have --- an algorithm everyone knows with no secret key, and yet it has uses in security.

6. ◎Foundations CRYPTANALSIS： 共有六種攻擊法，今依其難易度分成下述： (1) Ciphertext-only attack. Given： Deduce：Either ；or an algorithm to infer from (2) Known-plaintext attack. Given： Deduce：Either k, or an algorithm to infer from (3) Chosen-plaintext attack. Given：同上；where the cryptanalysis choose Deduce：同上

7. ◎Foundations (4) Adaptive-chosen-plaintext attack. 動態選取明密文：由第一次選取而得之結果去決定第二次選取之明 密文對（pair） (5)Chosen-ciphertext attack. 給予數對 “密文→明文” 而求出key k (6) Chosen-key attack. This is not an attack when you are given the key. It is strange and obscure, not very practical.

8. ◎Foundations Security of Cryptosystems All algorithms but one are theoretically breakable, given enough time and computing resources. If the time and money required to break an algorithm is more than the value of the encrypted data, then it is probably safe. An algorithm that is not breakable in practice is SECURE. Unconditionally secure VS. Computationally secure only a one-time pad is unbreakable given infinite resources(key 之長度大於明文長度). （針對 前者而言，這種僅用一次法的key之管理成本高） The amount of computing time and power required to recover the encryption key is called the WORK FACTOR, and is expressed as an order of magnitude.

9. ◎Foundations A cryptosystem is also called a CODE or a CIPHER. 參考資料：Substitution Ciphers & Transposition Cipher DES, Simple XOR均屬於此種類別， P XOR K = C C XOR K = P ( P XOR K ) XOR K = P Classical Cryptography This cryptosystem is called a stream cipher which is a classical cryptosystem.

10. 1. Foundations, including terminology and concepts of cryptography. 2. Cryptographic Protocols, including protocol build blocks (secure cryptographic module), basic protocols (key exchange, authentication, secret sharing, etc.), intermediate protocols (subliminal channel, group signature, key escrow, etc.), advanced protocols (zero-knowledge proofs, blind signature, oblivious transfer, etc.), esoteric(奧秘的) protocols (secure elections, anonymous broadcast, digital cash, etc.).

11. 3. Cryptographic Techniques, including key length, key management, and the using algorithms. 4. Cryptographic Algorithms, including mathematical backgrounds, DES and other block ciphers, one-way hash functions, public key cryptosystems. 5. Example Implementations, including some well-known commercial products and standards.