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**2007/416**

**Title:**

Compression Function Design Principles Supporting Variable Output Lengths from a Single Small Function

**Authors:**
Donghoon Chang, Mridul Nandi, Jesang Lee, Jaechul Sung, Seokhie Hong

**Abstract:**

In this paper, we introduce new compression function design principles supporting variable output lengths (multiples of size n). They are based on a function or block cipher with an n-bit output size. In the case of the compression function with a (t+1)n-bit output size, in the random oracle and ideal cipher models, their maximum advantages from the perspective of collision resistance are O(\frac{t^2q}{2^{tn}}+\frac{q^2}{2^{(t+1)n}}). In the case of t=1, the advantage is near-optimal. In the case of t>1, the advantage is optimal.

**ePrint:**
https://eprint.iacr.org/2007/416

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