Remarks on Gödel's Code as a Hash Function

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F10%3A00351385" target="_blank" >RIV/67985807:_____/10:00351385 - isvavai.cz</a>
Result on the web
<a href="http://www.sav.sk/journals/uploads/0317151904m-s.pdf" target="_blank" >http://www.sav.sk/journals/uploads/0317151904m-s.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Remarks on Gödel's Code as a Hash Function
Original language description
In this paper we analyze a simple hash function introduced in a popular book PopCo by Scarlett Thomas that is based on well known Gödel's numbering function. The numbering function is very slow for practical use, however it is widely used in foundationsof logic and computability theory. We show that the properties of the suggested hash function (computing the hash as a "shorter digest" of the long Gödel's number code) are not sufficient for cryptography. We introduce two ways how to construct meaningful collisions and in special cases also second-preimages. Further we propose a simple improvement of this hash function which prevents the simpler of the attacks, however this hasn't been successful for the second attack.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP202%2F10%2F1333" target="_blank" >GAP202/10/1333: NoSCoM: Non-Standard Computational Models and Their Applications in Complexity, Linguistics, and Learning</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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