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• Aes Round Key Generation
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AES is a symmetric key encryption cipher, and it is generally regarded as the “gold standard” for encrypting data. AES is NIST-certified and is used by the US government for protecting “secure” data, which has led to a more general adoption of AES as the standard symmetric key cipher of choice by just about everyone.

AES uses a key schedule to expand a short key into a number of separate round keys. The three AES variants have a different number of rounds. Each variant requires a separate 128-bit round key for each round plus one more.^{[note 1]} The key schedule produces the needed round keys from the initial key.

Round constants[edit]

The round constant rcon_i for round i of the key expansion is the 32-bit word:

where rc_i is an eight-bit value defined as:

where ${\displaystyle \oplus }$ is the bitwise XOR operator and constants such as 00₁₆ and 1B₁₆ are given in hexadecimal. Equivalently:

${\displaystyle r{c}_i=x^{i-1}}$

where the bits of rc_i are treated as the coefficients of an element of the finite field${\displaystyle \mathrm{G}\mathrm{F}(2)[\mathrm{x}]/({\mathrm{x}}^8+{\mathrm{x}}^4+{\mathrm{x}}^3+\mathrm{x}+1)}$, so that e.g. ${\displaystyle r{c}_{10}={36}_{16}={00110110}_2}$ represents the polynomial ${\displaystyle x^5+x^4+x^2+x}$.

AES uses up to rcon₁₀ for AES-128 (as 11 round keys are needed), up to rcon₈ for AES-192, and up to rcon₇ for AES-256.^{[note 2]}

The key schedule[edit]

Define:

Random key generator in python. Example import randomn = random.randomprint(n) OutputRunning the above code gives us the following result − 0.2112200 Generating Number in a RangeThe randint method generates a integer between a given range of numbers. Generating a Single Random NumberThe random method in random module generates a float number between 0 and 1.

• N as the length of the key in 32-bit words: 4 words for AES-128, 6 words for AES-192, and 8 words for AES-256
• K₀, K₁, .. K_N-1 as the 32-bit words of the original key
• R as the number of round keys needed: 11 round keys for AES-128, 13 keys for AES-192, and 15 keys for AES-256^{[note 3]}
• W₀, W₁, .. W_4R-1 as the 32-bit words of the expanded key^{[note 4]}

Also define RotWord as a one-byte left circular shift:

and SubWord as an application of the AES S-box to each of the four bytes of the word:

Then for ${\displaystyle i=0\dots 4R-1}$:

Notes[edit]

1. ^Non-AES Rijndael variants require up to 256 bits of expanded key per round
2. ^The Rijndael variants with larger block sizes use more of these constants, up to rcon₂₉ for Rijndael with 128-bit keys and 256 bit blocks (needs 15 round keys of each 256 bit, which means 30 full rounds of key expansion, which means 29 calls to the key schedule core using the round constants). The remaining constants for i ≥ 11 are: 6C, D8, AB, 4D, 9A, 2F, 5E, BC, 63, C6, 97, 35, 6A, D4, B3, 7D, FA, EF and C5
3. ^Other Rijndael variants require max(N, B) + 7 round keys, where B is the block size in words
4. ^Other Rijndael variants require BR words of expanded key, where B is the block size in words

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References[edit]

• FIPS PUB 197: the official AES standard (PDF file)

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External links[edit]

• schematic view of the key schedule for 128 and 256 bit keysfor 160-bit keys on Cryptography Stack Exchange

• Cryptography Tutorial

• Cryptography Useful Resources

• Selected Reading

The Data Encryption Standard (DES) is a symmetric-key block cipher published by the National Institute of Standards and Technology (NIST).

DES is an implementation of a Feistel Cipher. It uses 16 round Feistel structure. The block size is 64-bit. Though, key length is 64-bit, DES has an effective key length of 56 bits, since 8 of the 64 bits of the key are not used by the encryption algorithm (function as check bits only). General Structure of DES is depicted in the following illustration −

Since DES is based on the Feistel Cipher, all that is required to specify DES is −

• Round function
• Key schedule
• Any additional processing − Initial and final permutation

Initial and Final Permutation

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The initial and final permutations are straight Permutation boxes (P-boxes) that are inverses of each other. They have no cryptography significance in DES. The initial and final permutations are shown as follows −

Round Function

The heart of this cipher is the DES function, f. The DES function applies a 48-bit key to the rightmost 32 bits to produce a 32-bit output.

• Expansion Permutation Box − Since right input is 32-bit and round key is a 48-bit, we first need to expand right input to 48 bits. Permutation logic is graphically depicted in the following illustration −

• The graphically depicted permutation logic is generally described as table in DES specification illustrated as shown −

• XOR (Whitener). − After the expansion permutation, DES does XOR operation on the expanded right section and the round key. The round key is used only in this operation.

• Substitution Boxes. − The S-boxes carry out the real mixing (confusion). DES uses 8 S-boxes, each with a 6-bit input and a 4-bit output. Refer the following illustration −

• The S-box rule is illustrated below −

• There are a total of eight S-box tables. The output of all eight s-boxes is then combined in to 32 bit section.

• Straight Permutation − The 32 bit output of S-boxes is then subjected to the straight permutation with rule shown in the following illustration:

Key Generation

The round-key generator creates sixteen 48-bit keys out of a 56-bit cipher key. The process of key generation is depicted in the following illustration −

The logic for Parity drop, shifting, and Compression P-box is given in the DES description.

DES Analysis

The DES satisfies both the desired properties of block cipher. These two properties make cipher very strong.

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• Avalanche effect − A small change in plaintext results in the very great change in the ciphertext.

• Completeness − Each bit of ciphertext depends on many bits of plaintext.

During the last few years, cryptanalysis have found some weaknesses in DES when key selected are weak keys. These keys shall be avoided.

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DES has proved to be a very well designed block cipher. There have been no significant cryptanalytic attacks on DES other than exhaustive key search.