Keccakf1600

Keccakf1600 is a permutation function that operates on a 1600‑bit state and serves as the core component of the Keccak cryptographic hash family, most notably the SHA‑3 standard. The 1600‑bit state is organized as a 5 × 5 array of 64‑bit lanes, yielding a total of 25 lanes. Keccakf1600 performs a series of rounds; the standard implementation uses 24 rounds, each applying the same sequence of transformations.

Each round consists of five elementary steps in the following order: θ (Theta), ρ (Rho), π (Pi), χ (Chi), and iota (Iota). Theta computes parity across columns and adds it to each lane, ensuring diffusion of column information. Rho rotates each lane by a predetermined offset; Pi rearranges the positions of the lanes based on a fixed permutation. Chi applies a nonlinear function by XORing each lane with the conjunction of adjacent lanes, contributing to the function’s nonlinearity. Finally, Iota XORs a round constant with a single lane, providing round‑dependent variation.

The Keccakf1600 permutation is designed for high parallelism and efficient implementation on both software and hardware platforms. It achieves a substantial width—1600 bits—allowing for a large internal state that enhances resistance to collision and preimage attacks. Because its round structure contains both linear and nonlinear components, Keccakf1600 is regarded as having high cryptographic strength and is resistant to differential, linear, and algebraic attacks.

In SHA‑3, Keccakf1600 is repeatedly invoked as part of the sponge construction, which absorbs input data into the state and squeezes hash output from it. The permutation also underlies the SHAKE extendable‑output functions, enabling variable‑length outputs. Beyond hash functions, Keccakf1600 has been used in authenticated encryption modes such as the Ascon and Padlock families, where its properties provide security and performance benefits.