This episode provides a comprehensive overview of the Advanced Encryption Standard, or AES, a symmetric block cipher designed to replace DES for commercial and governmental applications.
Main Concepts and Theories
AES is a block cipher that operates on 128-bit data blocks. It supports key lengths of 128, 192, or 256 bits, leading to variants known as AES-128, AES-192, and AES-256. A crucial distinction of AES is that it does not employ a Feistel structure, unlike many earlier block ciphers. Instead, each full round of AES encryption involves four distinct transformation functions: byte substitution, permutation through row shifting, arithmetic operations over a finite field, and an XOR operation with a round key. The overall structure is complex, and for initial understanding, a simplified version of AES (often found in appendices or supplementary materials) can be very helpful.
Key Methodologies and Approaches
All arithmetic operations within AES are performed on 8-bit bytes, specifically within the finite field GF(2^8). This finite field arithmetic is foundational to AES. A field is a mathematical set where addition, subtraction, multiplication, and division are well-defined and always yield results within the set, including the existence of multiplicative inverses for all non-zero elements. For GF(2^n), elements are treated as polynomials of degree less than n with binary coefficients (0 or 1).
In AES, addition of two 8-bit bytes is simply a bitwise XOR operation. Multiplication is more involved, defined over GF(2^8) using a specific irreducible polynomial, m(x) = x^8 + x^4 + x^3 + x + 1. This means that if polynomial multiplication results in a degree higher than 7, it is reduced modulo m(x). Multiplication by powers of two can be achieved through a left shift followed by a conditional XOR with a constant derived from the irreducible polynomial.
Technical Details and Frameworks
The AES encryption process begins with a 128-bit plaintext block, which is arranged into a 4x4 byte "State" matrix. The input key is expanded into a key schedule, generating a distinct 128-bit round key for each round. The number of rounds (N) varies with the key length: 10 rounds for a 128-bit key, 12 for a 192-bit key, and 14 for a 256-bit key.
The cipher sequence involves an initial "AddRoundKey" transformation, followed by N-1 full rounds, and a final round. Each full round consists of four transformations applied to the State matrix:
1. Substitute Bytes Transformation: Each byte in the State matrix is replaced using a substitution box (S-Box), a non-linear byte substitution.
2. ShiftRows Transformation: The rows of the State matrix are cyclically shifted by different offsets. The first row is not shifted, the second row shifts one byte to the left, the third two bytes, and the fourth three bytes.
3. MixColumns Transformation: Each column of the State matrix is treated as a polynomial over GF(2^8) and multiplied by a fixed polynomial modulo x^4 + 1. This step provides diffusion.
4. AddRoundKey Transformation: The current round key is XORed with the State matrix, providing confusion.
The final round omits the MixColumns transformation. Decryption involves applying the inverse of these transformations in reverse order.
Important Insights and Findings
AES represents a robust and highly secure cryptographic standard. Its design choice to avoid the Feistel structure and process the entire data block at once contributes to its strength and efficiency. The careful selection of the irreducible polynomial for GF(2^8) was a deliberate design decision, aiming for optimal cryptographic properties. The algorithm's design ensures a strong "avalanche effect," meaning that a small change in the plaintext or key results in a significant and unpredictable change in the ciphertext, a critical property for modern ciphers. Implementation aspects also consider efficiency and resistance to various attacks.
