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On the invertibility of finite linear transducers

Published online by Cambridge University Press:  07 March 2014

Ivone Amorim ,
António Machiavelo  and
Rogério Reis
Ivone Amorim
Affiliation:
CMUP, Faculdade de Ciências da Universidade do Porto, Portugal. ivone.amorim@dcc.fc.up.pt; ajmachia@fc.up.pt; rvr@dcc.fc.up.pt
António Machiavelo
Affiliation:
CMUP, Faculdade de Ciências da Universidade do Porto, Portugal. ivone.amorim@dcc.fc.up.pt; ajmachia@fc.up.pt; rvr@dcc.fc.up.pt
Rogério Reis
Affiliation:
CMUP, Faculdade de Ciências da Universidade do Porto, Portugal. ivone.amorim@dcc.fc.up.pt; ajmachia@fc.up.pt; rvr@dcc.fc.up.pt
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Abstract

Linear finite transducers underlie a series of schemes for Public Key Cryptography (PKC) proposed in the 90s of the last century. The uninspiring and arid language then used, condemned these works to oblivion. Although some of these schemes were afterwards shown to be insecure, the promise of a new system of PKC relying on different complexity assumptions is still quite exciting. The algorithms there used depend heavily on the results of invertibility of linear transducers. In this paper we introduce the notion of post-initial linear transducer, which is an extension of the notion of linear finite transducer with memory, and for which the previous fundamental results on invertibility still hold. This extension enabled us to give a new method to obtain a left inverse of any invertible linear finite transducer with memory. It also plays an essencial role in the necessary and sufficient condition that we give for left invertibility of linear finite transducers.

Keywords

Linear transducersinvertibility of transducersautomata based cryptographytransducer injectivity with delay
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 1: Non-Classical Models of Automata and Applications (NCMA 2012) , January 2014 , pp. 107 - 125
Copyright
© EDP Sciences 2014

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