It has been proposed to use double-DES as a fixed-length collision- resistant hash function within the Merkle-Damgård transform, in the following way. Define the hash function h : {0,1}112 → {0,1}64 as h(x1||X2) = DES,,(DES-,(064)) where |¤1| = |x2| = 56. (a) Write down an actual collision in this fixed-length hash function. (b) In how much time is it possible to find a preimage for the hash function. That is, given some y € {0,1}64 show how to find a pair (x1, x2) such that h(x1||x2) = y. Make your attack as quick as possible. Does your attack make it possible to find a preimage that "makes sense" (say, one that contains an English word)? (c) What happens when h as above is used in the Merkle-Damgård transform? Find the most effective attack that you can think of.
It has been proposed to use double-DES as a fixed-length collision- resistant hash function within the Merkle-Damgård transform, in the following way. Define the hash function h : {0,1}112 → {0,1}64 as h(x1||X2) = DES,,(DES-,(064)) where |¤1| = |x2| = 56. (a) Write down an actual collision in this fixed-length hash function. (b) In how much time is it possible to find a preimage for the hash function. That is, given some y € {0,1}64 show how to find a pair (x1, x2) such that h(x1||x2) = y. Make your attack as quick as possible. Does your attack make it possible to find a preimage that "makes sense" (say, one that contains an English word)? (c) What happens when h as above is used in the Merkle-Damgård transform? Find the most effective attack that you can think of.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5.9 ILl has been proposed to use double-DES as a ſixed-length collision-
resistant hash function within the Merkle-Damgård transform, in the
following way. Define the hash function h : {0,1}112 .
h(x1||r2) = DES=, (DES,(064)) where |¤1| = |x2| = 56.
{0, 1}64 as
%3D
(a) Write down an actual collision in this fixed-length hash function.
(b) In how much time is it possible to find a preimage for the hash
function. That is, given some y e {0,1}64 show how to find a
pair (x1, x2) such that h(x1||x2) = y. Make your attack as quick
as possible. Does your attack make it possible to find a preimage
that "makes sense" (say, one that contains an English word)?
(c) What happens when h as above is used in the Merkle-Damgård
transform? Find the most effective attack that you can think of.
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