Feistel network

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A Feistel network is a construction to transform an arbitrary function into a permutation.

Definition

For any function $f:\{0,1\}^k \rightarrow \{0,1\}^k$ , we define the (single-layer) Feistel network of $f$ to be the function:

$F_f(x,y)=(y,x\oplus f(y))$ ,

where $\oplus$ denotes bitwise exclusive-or (XOR). Note that no matter what $f$ is, $F_f\,$ is a permutation over $\{0,1\}^{2k}\,$ .

A multi-layer Feistel network of functions $f_1, \ldots, f_t$ is simply the composition of their single-layer Feistel networks:

$F_{f_1,\ldots,f_t}(x,y)=F_{f_t}(\ldots(F_{f_1}(x,y))\dots)$

The functions $f_1,\ldots,f_t$ are called the round functions of the Feistel network.

See also

Luby-Rackoff construction

Retrieved from "http://crypto.cs.uiuc.edu/wiki/index.php/Feistel_network"

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