In thc Gibson schemc, the modulus N = p x ą is public, whilc its factors arc sccrct. The hashing function is defined as h(m) 9" mod N whcre g is a gcncrator of thc cyclic group Z. Let N = 4897 and 9 2231. Compute digests for the following two mcssages: 75676. Assumc that you have two colliding mcssages, show that it is possible to find factors ofN. Dcmonstrate that the knowledge of factors of N, allows m = 132748 and m' to find colliding messagcs.

Computer Networking: A Top-Down Approach (7th Edition)
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7. In the Gibson scheme, the modulus N = p x q is public, whilc its factors are secret. The
hashing function is defined as h(m) = 9 mod N wherc g is a gencrator of the cyclic
group Z. Let N =
4897 and 9 = 2231. Computc digests for thc following two mcssages:
m = 132748 and m'
= 75676. Assumc that you have two colliding mcssages, show that it
is possible to find factors of N. Dcmonstrate that thc knowledge of factors of N, allows
to find colliding mcssagcs.
Transcribed Image Text:7. In the Gibson scheme, the modulus N = p x q is public, whilc its factors are secret. The hashing function is defined as h(m) = 9 mod N wherc g is a gencrator of the cyclic group Z. Let N = 4897 and 9 = 2231. Computc digests for thc following two mcssages: m = 132748 and m' = 75676. Assumc that you have two colliding mcssages, show that it is possible to find factors of N. Dcmonstrate that thc knowledge of factors of N, allows to find colliding mcssagcs.
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