Substitution Cryptography is a #cryptographic method that encrypt a message by replacing every text with an alternate text based on their natural or mathematical relationship between each other.
All followings #algorithm or devices utilise substitution in producing their ciphertext:
Vernam Cipher is a #Substitution Cryptographic #algorithm invented by Gilbert Vernam in 1918. It works on the binary data with bit-wise XOR operation (or in Modular Arithmetic, \(\mod 2\)) and chooses a key with no statistical relationship with the plaintext. It is widely adopted as it could be implemented easily using hardware circuits. The encryption scheme is formalised using the following equations:
Shift Cipher or Caesar Cipher, named after Julius Caesar, is a simple #Substitution Cryptographic #algorithm that simply shifts one letter of the alphabet to a set number of places in the alphabet for another letter (by default, shift 3 places). For example, if the shift value is 4, this means that the letter need to be shifted to the right 4 times, meaning the letter “A” would be “E” in the ciphertext.
Rotor Machine is an electro-mechanical stream cipher# device that could perform #Substitution Cryptography with a more complex scheme.
Product Cipher is a cipher that composed of both #substitution (S-box) and #permutation (P-box). Introduced by Claude Shannon, it is the backbone for the modern Block Cipher. It provides diffusion and confusion of message and key.
Polyalphabetic Cipher is a Substitution Cryptographic #algorithm where the same plaintext letter could be replaced by several ciphertext letters depending on its position in plaintext. The relationship between a character in the plaintext and a character in the ciphertext is one-to-many, thus make it hard to crack using Frequency Analysis# and more secure than Monoalphabetic Cipher.
Output Feedback is a stream mode of operation# of #Data Encryption Standard (DES) and #Advanced Encryption Standard (AES) where the preceding encryption output of the permuted encrypted initialisation value (feedback) is used as the input to the encryption #algorithm. The feedback is indenpendent of message thus can be computed in advance. Full blocks are used. It is pretty similar to Cipher Feedback (CFB) otherwise.
One-Time Pad, or sometimes called One-Time Vernam Cipher#, is a #Substitution Cryptographic #algorithm that uses a single-use secret key for encrypting. It requires the key to be as long as the plaintext and random. Thus, guarantees an Unconditional Security# to the ciphertext. However, it does face some security concerns over secure key distribution and key generation for randomness. It is only used for low bandwidth and very high security purposes.
Monoalphabetic Cipher is a #Substitution Cryptographic #algorithm that shuffle the letters arbitrarily (random) which has a key size of 26 letters. The total number of keys are \(26! = 4.03 \times 10^{26}\). However, since in Monoalphabetic Cipher the relationship between the letter in a plaintext to the letter in a ciphertext is always one-to-one, it is vulnerable to Frequency Analysis# due to the fact the frequency of the letters is not altered.
Linear Cryptanalysis is an #Analytic Attacks approximate the non-linearity with linear equations (finding the linear approximation). This is focus on the S-boxes’ non-linearity.
First, it starts its cipher process halving input blocks, which then perform substitution# on left data half based on round function with right halve and subkey as parameters. After that, it performs a permutation# by swapping the halves. The process is then repeated for multiple rounds. The process is shown as formula below:
ECB is a block mode of operation# from #Data Encryption Standard (DES) and #Advanced Encryption Standard (AES) where each block of plaintext bits is encoded using Substitution# independently# with the same key. The formal equation for the encryption is as follow:
Differential Cryptanalysis is an #Analytic Attacks against Feistel Cipher Structure# by comparing the input (plaintext) and output (ciphertext) differences. It is focus on the non-linearity of the cipher especially the S-boxes.
The substitution on the left half is done by XORing the output of the rounding function with the right half and a subkey as parameters. The right half, size of 32-bit, will be expanded or permuted using Expansion table (E table) to produce a 48-bit data which then XORs with the subkey. After that, substitution# will be done on the data with 8 S-boxes (which is the backbone for the DES security guarantees) that map 6 to 4 bits producing a 32-bit data which feed it to another permutation (XOR with the left half later).
AES processes data as block of 4 columns of 4 bytes. It will then operate on the entire data block in every round (up to 9, 11, 13 rounds) with byte substitution#, shift rows#, mix columns (substitution using matrix multiply of group), and add round key (XOR the data block with key) which view the data block as alternate XOR key and scramble data bytes. Decryption is done in reverse to encryption process.