How to construct random functions

How to Construct Cryptosystems and Hash Functions in Weakened Random Oracle Models

In this paper, we discuss how to construct secure cryptosystems and secure hash functions in weakened random oracle models. The weakened random oracle model (WROM), which was introduced by Numayama et al. at PKC 2008, is a random oracle with several weaknesses. Though the security of cryptosystems in the random oracle model, ROM, has been discussed sufficiently, the same is not true for WROM. A...

How to Construct Pseudorandom Permutations from Single Pseudorandom Functions

The paper examines permutation generators which are designed using four rounds of the Data Encryption Standard and a single pseudorandom function. We have proved that such generators are pseudorandom only if the pseudorandom function is used internally at least five times. The proof is given using two different approaches: deterministic and probabilistic. Some cryptographic implications are als...

How to Construct Double-Block-Length Hash Functions

In this article, it is discussed how to construct a com­ pression function with 2n-bit output using a com­ ponent function with n-bit output. The compo­ nent function is either a smaller compression func­ tion or a block cipher. Some constructions are pre­ sented which compose collision-resistant hash func­ tions: Any collision-finding attack on them is at most as efficient as the birthday atta...

How To Construct Extractable One-Way Functions Against Uniform Adversaries

A function f is extractable if it is possible to algorithmically “extract,” from any program that outputs a value y in the image of f, a preimage of y. When combined with hardness properties such as one-wayness or collision-resistance, extractability has proven to be a powerful tool. However, so far, extractability has not been explicitly shown. Instead, it has only been considered as a nonstan...

How to Construct Pseudorandom Functions Extracts from Foundations of Cryptography1