12 Symmetric cryptosystem. Aes

The Advanced Encryption Standard (AES), the block cipher ratified as a standard by National Institute of Standards and Technology of the United States (NIST), was chosen using a process lasting from 1997 to 2000 that was markedly more open and transparent than its predecessor, the aging Data Encryption Standard (DES). This process won plaudits from the open cryptographic community, and helped to increase confidence in the security of the winning algorithm from those who were suspicious of backdoors in the predecessor, DES.

DEscryption of cipher

AES is based on a design principle known as a substitution-permutation network, and is fast in both software and hardware.^[6] Unlike its predecessor DES, AES does not use aFeistel network. AES is a variant of Rijndael which has a fixed block size of 128 bits, and a key size of 128, 192, or 256 bits. By contrast, the Rijndael specification per se is specified with block and key sizes that may be any multiple of 32 bits, both with a minimum of 128 and a maximum of 256 bits.

AES operates on a 4×4 column-major order matrix of bytes, termed the state, although some versions of Rijndael have a larger block size and have additional columns in the state. Most AES calculations are done in a special finite field.

The key size used for an AES cipher specifies the number of repetitions of transformation rounds that convert the input, called the plaintext, into the final output, called the ciphertext. Thenumberofcyclesofrepetitionareasfollows:

12. ycles of repetition for 128-bit keys.12 cycles of repetition for 192-bit keys.,14 cycles of repetition for 256-bit keys.

Each round consists of several processing steps, including one that depends on the encryption key itself. A set of reverse rounds are applied to transform ciphertext back into the original plaintext using the same encryption key.

13.Block cipher modes

Electronic Codebook Mode (ECB)

This is the simplest and older mode of operation. Each plaintext block is encrypted/decrypted individually. Resulting in a cipher text that is the same for each given plaintext and key m so Identical plaintexts will produce identical ciphertexts

Cipher Blockchaining Mode (CBC)

This mode uses an Initialization Vector (IV) and chains all blocks together by XORing the output of the encryption block with the next plaintext block.

P_i denotes plaintext, C_i denotes ciphertext

C_i = E(K, P_iÅ C_i-1) for i = 1, 2, …, k

• In the above equation, when i = 1 we get

C₁ = E(K, P₁Å C₀)

The value C₀ is known as the Initialization Vector or IV.

Cipher Feedback Mode (CFB)

CFB is a stream cipher as opposed to block cipher since it uses only 8-bit blocks. This mode allows transmission of messages of less bits than the blocksize (for example used for interactive terminal sessions).

Output Feedback Mode (OFB)

OFB is also a stream cipher. OFB is very similar to CFB, except that the output of the encryption function is fed back where as in CFB the ciphertext is fed back and errors do not propagate. It is also more vulnerable to attack than cipher feedback. In output feedback, the output of the DES block cipher is fed back as the input to produce the next block. Consecutive bits of the block cipher output are exclusive ORed with the plaintext to produce the ciphertext. The algorithms for encryption and decryption are identical. In OFB, unlike CBC, the key K0 is chosen from the IV and Ki = E(K,Ki-1) for i = 1, 2, …, k is calculated using a shift register

Ci = Pi Å Ki

CTR stands for Counter mode

It is one of the oldest methods available, even before DES was developed. CTR is a stream cipher

NIST standardized CTR in 2001. In CTR, the user chooses a nonce as an IV and then each key value is chosen by concatenating the nonce with the counter value: Ki = E(K,nonce||i) CTR encryption and decryption functions are identical. CTR lends itself for parallel processing since each Ci = Pi Å Ki and Ki does not depend on Ki-1.