Title: Search problems and search for collisions in hash functions Author: Samuel Čarnoký Department: The Department of Algebra Supervisor: prof. RNDr. Jan Krajíček, DrSc. Supervisor's e-mail address: krajicek@karlin.mff.cuni.cz Abstract: Central points of this work are NP search problems and the existence of reductions amog them in the relativised world. Absolute separation would separate N from NP. In particular, we talk about the problem of finding collisions in hash functions that must exist due to the famous pigeonhole principle. We present a brief introduction into the topic, we define various NP search problems and recall reductions and separations. Reduction of weak version of PHP to a problem of finding a homogeneous subgraph is described and our own results are presented in the form of reduction of another variant of PHP to a problem related to finding paths in a graph. We talk about reducing the task of finding collisions in multiple functions into finding a collision in one function. Keywords: NP search, reductions, pigeonhole principle, oracles
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:297912 |
| Date | January 2011 |
| Creators | Čarnoký, Samuel |
| Contributors | Krajíček, Jan, Pudlák, Pavel |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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