Keccak hash function
Understanding this Keccak hash function and all it variant
Why is Keccak (SHA-3) a One-Way Hash Function?
A one-way function means that given an output h = H(m), it is computationally infeasible to find the original input m (preimage resistance). Keccak achieves this due to the following technical properties:
1. Keccak’s Sponge Construction Prevents Reversal
Keccak uses a sponge construction, which has two phases:
Absorption: Message blocks are XORed into the state and transformed using Keccak-f permutations.
Squeezing: Output is extracted from the state after several irreversible transformations.
Once data is mixed into the internal state, it is non-linearly transformed multiple times, making it impossible to isolate the original input.
The state contains more bits (1600 bits) than the output (e.g., 256 bits in SHA3-256), meaning information is lost, making inversion impossible.
2. The Keccak-f Permutation is Cryptographically Strong
The Keccak-f permutation consists of five steps in each round, all contributing to non-invertibility:
1. Theta (Parity Mixing)
Each bit is mixed with bits from two other columns.
Small changes in input cause widespread diffusion across the state.
2. Rho (Bitwise Rotation)
Each word is rotated by a unique offset, breaking alignment with previous transformations.
3. Pi (Lane Permutation)
Rearranges the state non-linearly, making it impossible to track input positions.
4. Chi (Nonlinear Layer)
Applies an AND-XOR transformation, preventing algebraic attacks (no easy linear equations for solving input).
5. Iota (Round Constant Injection)
Ensures each round is unique, preventing cycles and fixed points.
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