On the invertibility of finite linear transducers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 1, pp. 107-125.

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.

DOI : https://doi.org/10.1051/ita/2014004
Mots clés : linear transducers, invertibility of transducers, automata based cryptography, transducer injectivity with delay
@article{ITA_2014__48_1_107_0,
     author = {Amorim, Ivone and Machiavelo, Ant\'onio and Reis, Rog\'erio},
     title = {On the invertibility of finite linear transducers},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {107--125},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {1},
     year = {2014},
     doi = {10.1051/ita/2014004},
     mrnumber = {3195791},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2014004/}
}
Amorim, Ivone; Machiavelo, António; Reis, Rogério. On the invertibility of finite linear transducers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 1, pp. 107-125. doi : 10.1051/ita/2014004. http://www.numdam.org/articles/10.1051/ita/2014004/

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