In: Tatra Mountains Mathematical Publications, vol. 47, no. 3
Michal Mikuš - Petr Savicky
Details:
Year, pages: 2010, 67 - 80
Keywords:
Gödel numbering function, hash function, integer relation algorithm,
rational reconstruction.
About article:
In this paper we analyze a simple hash function introduced in a popular book
\emph{PopCo} by Scarlett Thomas that is based on
well known Gödel's numbering function.
The numbering function is very efficient for practical use,
however it is widely used in foundations of logic
and computability theory.
We show that the properties of the suggested hash function
(computing the hash as a ``shorter digest" of the \emph{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 simplest of the attacks,
however it does not eliminate the other attacks.
How to cite:
ISO 690:
Mikuš, M., Savicky, P. 2010. Remarks on Gödel's code as a hash function. In Tatra Mountains Mathematical Publications, vol. 47, no.3, pp. 67-80. 1210-3195.
APA:
Mikuš, M., Savicky, P. (2010). Remarks on Gödel's code as a hash function. Tatra Mountains Mathematical Publications, 47(3), 67-80. 1210-3195.