Cryptography Unit 5a Advanced Encryption Standard (AES)

Cryptography Notes

Unit 5: Advanced Encryption Standard (AES)

General Information

  • Known initially as Rijndael.

  • Developed in 2001 by Vincent Rijmen and Joan Daemen.

  • Recognized as the state-of-the-art cryptosystem as of 2018.

  • It is classified as a private key cryptosystem.

  • Supports three different key lengths: 128 bits, 192 bits, and 256 bits.

  • Operates as a block cipher without reliance on the Feistel structure.

  • Values (plaintext, key, ciphertext) are stored in matrix form.

Definitions and Structure

  • AES Definition: A word is considered a unit of data.

  • AES operates with a number of rounds based on key length:

    • 10 rounds for 128-bit keys.

    • 12 rounds for 192-bit keys.

    • 14 rounds for 256-bit keys.

Block Size

  • Block Size in AES: The size of a block in the AES cryptosystem is 128 bits.

    • Optionally, if the size of the plaintext or key block is less than 128 bits, it must be padded with 0x00 to increase the size to 128 bits.

Encryption Process

  • The general steps in the AES encryption process for a 128-bit plaintext block involve:

    • Adding Round Key: First operation takes place with a key.

    • S-BOX (Substitution Bytes): Each byte is substituted based on a fixed table.

    • Shift Rows: Rows of the state are shifted left.

    • Mix Columns: Each column is mixed.

Detailed Steps in Each Round

  • For each round, the following occurs:

    • Substitution (S-BOX)

    • Implements non-linear substitution: each byte is replaced with another byte according to the S-BOX.

    • The S-BOX is a 16x16 lookup table that achieves cryptographic strength by resisting linear and differential cryptanalysis.

    • Shift Rows: Circular shifting of the rows in the state matrix. The first row is unchanged, the second row is shifted left by 1 byte, the third row by 2 bytes, and the fourth row by 3 bytes.

    • Mix Columns: Involves a linear transformation where each column is treated as a polynomial and multiplied with a fixed polynomial modulo an irreducible polynomial.

    • Add Round Key: Involves bitwise XORing with the round key.

Component Operations


Add Round Key Operation

  • Works using the XOR operation; input plaintext and the private key are both 128 bits long.

  • Example: If input plaintext block and the private key are:

Plaintext:  0  1  1  1  0  1  1  1  0
Key:       0  1  1  1  0  1  1  1  0  
Result:    0 XOR 0  ,  1 XOR 1  [Results in the new state]


Substitution Bytes Operation (S-BOX)

  • Involves looking up each byte in the S-BOX.


  • The S-BOX transformation is defined as follows:

    Row

    Col

    Value


    00

    00

    63


    00

    01

    7C


    …

    …

    …


    …

    …

    …

    • Purpose: Ensures resistance against cryptoanalysis techniques; values are predefined to obfuscate data effectively.

    Shift Rows Operation

    • Efficient circular left shift of the rows. Explained as:

    • Row 1: No shift.

    • Row 2: 1 byte left.

    • Row 3: 2 bytes left.

    • Row 4: 3 bytes left.

    • #### Mix Columns Operation

    • A mathematical operation that applies a matrix transformation.

    • The mix columns operation consists of multiplying the state matrix by a fixed polynomial based matrix, representing it in GF(2^8).

    • Example Calculation:

    Input Matrix: [02 03 01 01] * [Input Column] = Result Matrix

    Example of Mix Columns Calculation

    • Calculation for the first row and column produces a resultant matrix based on the polynomial multiplication followed by XOR operations, where:

      • For example, converting hex values into a polynomial and performing the multiplication yields the results.

    Questions and Answer Section

    • Question 1: What is the size of a block in the AES cryptosystem?

      • Answer Choices:

      • 64 bits

      • 128 bits ✅

      • 256 bits

    • Question 2: Why are predefined values used in the S-Box?

      • Predefined values enhance security by preventing parallel algorithms from successfully cracking the cryptosystem and ensuring resistance to linear and differential cryptoanalysis.

    Final Notes

    • The AES is crucial for secure communication and data protection and continues to be highly relevant in the ongoing advancements in cryptographic practices.

    • Continuous evaluations award it with the reputation of being one of the strongest encryption techniques available today.

    References

    • Additional examples, calculations, or videos may be relevant for further illustration, including documentations and graphical representations.