网络与信息安全——知识整理（2）

The Traditional Symmetric-Key Ciphers

 

Define P as the plaintext, C as theciphertext, and K is the key, than:

Encryption: C=E_k(P)

Decryption: P=D_k(C)

In which: D_k(E_k(x))=E_k(D_k(x))=x

 

The Kerckhoff’s Principle

The resistance of the cipher to attack mustbe based on the secrecy of the key only.

 

The Cryptanalysis Attacks

Cryptanalysis is the science and art ofbreaking ciphered code, which includes:

1. Ciphertext-only Attack

2. Known-plaintext Attack

3. Chosen-plaintext Attack

4. Chosen-ciphertext Attack

 

The Substitution Ciphers

A substitution cipher replaces one symbolwith another.

 

1. Monoalphabetic Substitution Ciphers

In monoalphabetic substitution, therelationship between a symbol in plaintext and ciphertext is always one-to-one.

 

a. The Additive Cipher (Shift Cipher/CaesarCipher)

Encryption: C = (P + K) mod 26

Decryption: P = (C – K) mod 26

Note that the plaintext, ciphertext and keyare integers in Z₂₆.

 

b. The Multiplicative Ciphers

Encryption: C = (P * K) mod 26

Decryption: P = (C * K^-1) mod 26

Note that the plaintext and ciphertext areinteger in Z₂₆, and the key is an integer in Z₂₆* whichhas only 12 members: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25.

 

c. The Affine Ciphers

Encryption: C = (P * K₁ +K₂)mod 26

Decryption: P = ((C – K₂) * K₁^-1)mod 26

Note that the K₁ is from Z₂₆*and the K₂ is from Z₂₆. So the size of key domain is26*12=312.

 

2. Polyalphabetic Substitution Ciphers

In polyalphabetic substitution, therelationship between a symbol in plaintext and ciphertext is one-to-many.

 

a. Autokey Cipher

P = P₁P₂P₃…

C = C₁C₂C₃…

K = (k₁, P₁, P₂,…)

Encryption: C_i = (P_i+ K_i) mod 26

Decryption: P_i = (C_i –K_i) mod 26

 

b. Vigenere Cipher

P = P₁P₂P₃…

C = C₁C₂C₃…

K = [(k₁, k₂, …, k_m),(k₁, k₂, …, k_m), …]

Encryption: C_i = (P_i+ K_i) mod 26

Decryption: P_i = (C_i –K_i) mod 26

 

c. Hill Cipher

Define K as matrix:

K = [(k₁₁, k₁₂, …, k_1m),(k₂₁, k₂₂, …, k_2m), …, (k_m1, k_m2,…, k_mm)]

Encryption: C = PK

Decryption: P = CK^-1

Note that P and C are also matrix, and Kand be computed as K = P^-1C.

 

d. One-Time Pad Cipher

Each plaintext symbol is encrypted with akey randomly chosen from key domain. In this cipher, the key has same size asthe plaintext and is chosen completely in random.

 

The Transposition Ciphers

It does not substitute one symbol for another,but change its location instead.

 

1. Keyless Transposition Ciphers

a. Rail Fence Cipher: the ciphertext iscreated reading the pattern row by row.

 

2. Keyed Transposition Ciphers

This method permute the characters by usingwriting plaintext in one way and reading it in another way, and it is done onthe whole plaintext to create the whole ciphertext. Or first divide the wholeplaintext into blocks that has predetermined size, and then permute thecharacter in each block separately with a key.

 

3. Combining Two Approaches

It combines keyed transposition method andkeyless transposition method into one.

 

The Stream And Block Ciphers

1.Stream Ciphers

In a stream cipher, encryption anddecryption are done one symbol at a time, like this:

P = P₁P₂P₃;C = C₁C₂C₃; K = (k₁, k₂,k₃, …) then

C₁ = E_k1(P₁),C₂ = E_k2(P₂), C₃ = E_k3(P₃)

 

2. Block Cipher

In a block cipher, a group of plaintextsymbols are encrypted together to create a group of ciphertext with a singlekey.

 

In practice, Blocks of plaintext areencrypted individually with a stream of keys. In other word, the cipher isblock cipher when looking at the individual blocks, but a stream cipher whenlooking at the whole message and considering each block as a single unit.