Cryptography · Cluster
Symmetric Ciphers
Block and stream cipher design.
- 01 Why a Feistel Round Function Need Not Be Invertible The two-branch construction that turns any function into a permutation, why decryption reuses the encryption circuit, and what the halved diffusion rate costs.
- 02 The AES State Matrix: Byte Ordering, ShiftRows, and MixColumns How sixteen key bytes map onto a four-by-four matrix, why the row shift moves different distances, and what MixColumns does to a column as a polynomial.
- 03 Key Schedules: Why Subkeys Cannot Be Independent The key expansion that derives a round key from a short master key, the nonlinearity it must add, and the related-key and slide attacks that punish weak expansion.
- 04 Constructing an S-Box: Field Inversion and Differential Uniformity Why the AES substitution table is an inverse map in GF(2^8) followed by an affine transform, and how differential uniformity bounds the best characteristic.
- 05 Diffusion and Branch Numbers in Block Cipher Design How the wide-trail strategy counts active S-boxes across rounds, why a branch number of five bounds a four-round characteristic, and where the bound stops applying.
- 06 ARX Ciphers: Carry Chains as the Only Nonlinearity Why modular addition provides nonlinearity in add-rotate-xor designs, how carries propagate as a probabilistic process, and why diffusion is measured in bits.
- 07 LFSR Keystream Generators and the Linearity That Must Be Broken Why a shift register with linear feedback is a perfect pseudorandom generator and a useless cipher, and how combining several of them buys nonlinearity.
- 08 Differential and Linear Cryptanalysis as Trail Counting The two classical attacks reduce to finding high-probability differentials and high-bias linear approximations, and both are bounded by the same active S-box count.
- 09 Constant-Time AES: Removing the Secret-Dependent Table Lookup Why a 256-byte S-box leaks key bits through cache behaviour, and how bit-slicing and vector permutes replace the lookup without changing the cipher.
- 10 Tweakable Block Ciphers and the Cost of Sector Independence How a public tweak makes one key behave like many, why the tweak must enter before the first round, and what XTS and Threefish give up to get it.