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On the invertibility of finite lineartransducers

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 tobe insecure, the promise of a new system of PKC relying on different complexityassumptions is still quite exciting. The algorithms there used depend heavily on theresults of invertibility of linear transducers. In this paper we introduce the notion ofpost-initial linear transducer, which is an extension of the notion of linear finitetransducer with memory, and for which the previous fundamental results on invertibilitystill hold. This extension enabled us to give a new method to obtain a left inverse of anyinvertible linear finite transducer with memory. It also plays an essencial role in thenecessary and sufficient condition that we give for left invertibility of linear finitetransducers.

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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References

Diffie, W., The First Ten Years of Public-Key Cryptography. Proc. IEEE 76 (1988) 560–577. Google Scholar
Haiwen, O. and Zongduo, D., Self-Injective Rings and Linear (Weak) Inverses of Linear Finite Automata over Rings. Science in China, Series A 42 (1999) 140–146. Google Scholar
N. Jacobson, Basic Algebra I. W H Freeman & Co (1985).
Massey, J.L. and Slain, M.K., Inverses of Linear Sequential Circuits. IEEE Trans. Comput. C-17 (1968) 330–337. Google Scholar
Nerode, A., Linear Automaton Transformations. Proc. Amer. Math. Soc. 9 (1958) 541–544. Google Scholar
M. Newman, Integral Matrices. Academic Press (1972).
Tao, R., Invertible Linear Finite Automata. Sci. Sinica XVI (1973) 565–581. Google Scholar
R. Tao, Invertibility of Linear Finite Automata Over a Ring. Automata, Languages and Programming, in vol. 317 of Lect. Notes Comput. Sci. Springer Berlin, Heidelberg (1988) 489–501.
R. Tao, Finite Automata and Application to Cryptography. Springer Publishing Company, Incorporated (2009).
Tao, R. and Chen, S., A Finite Automaton Public Key Cryptosystem and Digital Signatures. Chinese J. Comput. 8 (1985) 401–409. (in Chinese). Google Scholar
Tao, R. and Chen, S., A Variant of the Public Key Cryptosystem FAPKC3. J. Netw. Comput. Appl. 20 (1997) 283–303. Google Scholar
Tao, R. and Chen, S., The Generalization of Public Key Cryptosystem FAPKC4. Chinese Sci. Bull. 44 (1999) 784–790. Google Scholar
Tao, R., Chen, S. and Xuemei, C., FAPKC3: A New Finite Automaton Public Key Cryptosystem. J. Comput. Sci. Techn. 12 (1997) 289–305. Google Scholar
Villard, G., Generalized subresultants for computing the Smith normal form of polynomial matrices. J. Symb. Comput. 20 (1995) 269–286. Google Scholar
Zongduo, D. and Dingfengd, Y., Weak Invertibility of Linear Finite Automata I, Classification and Enumeration of Transfer Functions. Sci. In China (Series A) 39 (1996) 613–623. Google Scholar
D. Zongduo, Y. Dingfeng and K.Y. Lam, Weak Invertibility of Finite Automata and Cryptanalysis on FAPKC. Advances in Cryptology – AsiaCrypt’98, in vol. 1514 of Lect. Notes Comput. Sci. Edited by K. Ohta and D. Pei. Springer-Verlag (1998) 227–241.
Zongduo, D., Dingfengd, Y., Qibin, Z. and Haiwen, O., Classification and Enumeration of Matched Free Response Matrices of Linear Finite Automata. Acta Math. Sinica, New Ser. 13 (1997) 133–144. Google Scholar