### Transfinite Cryptography

Jacques Patarin

##### Abstract

\begin{abstract} Let assume that Alice, Bob, and Charlie, the three classical people of cryptography are not limited anymore to perform a finite number of computations on real computers, but are limited to $\alpha$ computations and to $\alpha$ bits of memory, where $\alpha$ is a fixed infinite cardinal. For example $\alpha = \aleph _0$ (the countable cardinal, i.e. the cardinal of $\mathbb {N}$ the set of integers), or $\alpha = \mathfrak {C}$ (the cardinal of the set $\mathbb {R}$ of real numbers). Is it possible to do secret key cryptography? Public key cryptography? Encryption? Authentication? Signatures? Is it possible to generalize the notion of one way function? The aim of this paper is to give some elements of answers to these questions. We will see for example that for secret key cryptography there are some simple solutions. However for public key cryptography the results are much less clear. \end{abstract}

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Cryptography with infinite computations
Contact author(s)
valerie nachef @ u-cergy fr
History
Short URL
https://ia.cr/2010/001

CC BY

BibTeX

@misc{cryptoeprint:2010/001,
author = {Jacques Patarin},
title = {Transfinite Cryptography},
howpublished = {Cryptology ePrint Archive, Paper 2010/001},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/001}},
url = {https://eprint.iacr.org/2010/001}
}

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