Classical cryptosystem -- substitution and replacement

One 、 Introduction and classification

1. Introduce ：

The classical code period is generally considered to be from ancient times to 19 The end of the century , The level of productivity was low during this period , encryption 、 The decryption method is mainly based on paper 、 A pen or simple instrument , The ciphers proposed and used in this period are called classical ciphers . Classical cryptography is the primary stage of the development of cryptography . Although most classical passwords are simple , But because of its poor security , At present, there are few applications . Study the principles of classical cryptography , Help to understand 、 Construct and analyze modern ciphers . replace ( substitution) And replacement (permutation) Are two basic processing techniques used in classical cryptography , They are also widely used in modern cryptography .

2. implementation technique ：

• Replace   Replace clear text characters with other letters 、 Numbers or symbols
• substitution   The letters of plaintext are the same , But it was disrupted

3. classification

• Replace the password
  • Single table substitution code
  • Multiple tables replace passwords
• Replace password

Two 、 Replace the password

1. Single table substitution code

(1). Shift code

   Ek(P): Ci = (Pi+k) mod n, Dk(P): Pi = (Ci-k) mod n, 

    among Ek For encryption algorithms ,Pi In plain text ,Ci For the cipher ,k A key ,n Is the number of letters ,Dk For decryption algorithm .

    If it is a substitution between English letters , It can also be written in the following form ：

   Ci = (Pi + k) mod 26     Pi = (Ci - k) mod 26, among k∈[0,25]

    The Caesar code Ci = (Pi + 3) mod 26 It is a shift substitution cipher .

(2). Affine code

   Ek(P) = (aPi + b) mod m

(3). Replace the password

    Means that each letter is composed of the other one alphabet ( The mapping from plaintext letters to ciphertext letters ) Encryption of letters in

    How to decipher ： Exhaustive key method 、 Statistical analysis ( Use the laws of language )      

2. Multiple tables replace passwords

(1). Virginia code

The Virginia code consists of some Caesar codes with different offsets , The offset of each plaintext letter is determined by a given key . Such as clear text "abcd"( The key is plan), Clear text letter a The offset of is p Number of digits 15.a The offset 15 Bit followed by p,p It is the ciphertext letter corresponding to the plaintext letter .

Ci = (Pi + ki) mod 26

The Virginia code is also seen as based on a two-dimensional password table , The plaintext letter and the corresponding key letter are the number of rows and columns respectively , The corresponding letter found in the table is the ciphertext letter

give an example ：

Plaintext ：howareyou
secret key ：mine

Plaintext (P)	H	O	W	A	R	E	Y	O	U
secret key (k)	M	I	N	E	M	I	N	E	M
Ciphertext (C)	T	W	J	E	D	M	L	S	G

 

Deciphering skills ：

• The result of object substitution is the same if the interval is an integer multiple of the key length
• The substitution at the position where the interval is an integral multiple of the key length is a single table substitution

(2). One secret at a time

Using a random set of non repeating characters as the output ciphertext . Once the transformed input ciphertext is used , This input ciphertext is no longer used in any other message ( So it's disposable ). The length of the input ciphertext is equal to the length of the plaintext of the original message .

Here are the main steps .

1. Take each plaintext letter as a number in increasing order ,A=0,B=1 wait .

2. Do the same for each letter in the input plaintext .

3. Add each letter in the plaintext to the corresponding letter in the key .

4. If the sum obtained is greater than 26, Then subtract 26 (mod 26)

5. Convert and to letters , To get the ciphertext .

3、 ... and 、 Replace password

The replacement password is ⼀ Through ⼀ Set rules to change the order of characters in a string from ⽽ Implementation of cryptographic algorithms for encryption .

And the difference between substitution password ：

Substitution password is to replace plaintext letters with different ciphertext letters , The generated ciphertext may contain letters that are not contained in the plaintext , The replacement password is just to disturb the position and order of the plaintext letters

There are many kinds of replacement passwords , Give an example of ： Write the ciphertext line by line in the table , Read in column by column order , Such as clear text :howareyouImfinethankyouandyouhaha, Then ciphertext ：hfuoiawnnaedrtyehoyauonhukaiyhmoa.

H	O	W	A	R	E	Y	O	U	I	M
F	I	N	E	T	H	A	N	K	Y	O
U	A	N	D	Y	O	U	H	A	H	A