By Gul Agha (auth.), Traian Muntean, Dimitrios Poulakis, Robert Rolland (eds.)
This booklet constitutes the refereed lawsuits of the fifth foreign convention on Algebraic Informatics, CAI 2013, held in Porquerolles, France in September 2013. the nineteen revised complete papers provided including five invited articles have been rigorously reviewed and chosen from quite a few submissions. The papers conceal subject matters similar to information types and coding thought; primary facets of cryptography and defense; algebraic and stochastic types of computing; good judgment and application modelling.
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Extra info for Algebraic Informatics: 5th International Conference, CAI 2013, Porquerolles, France, September 3-6, 2013. Proceedings
31–46. Springer, Heidelberg (2008) 18. : Smaller decoding exponents: Ball-collision decoding. In: Rogaway, P. ) CRYPTO 2011. LNCS, vol. 6841, pp. 743–760. Springer, Heidelberg (2011) 42 P. V´eron 19. : Smaller decoding exponents: Ball-collision decoding. In: Rogaway, P. ) CRYPTO 2011. LNCS, vol. 6841, pp. 743–760. Springer, Heidelberg (2011) 20. : Wild McEliece. R. ) SAC 2010. LNCS, vol. 6544, pp. 143–158. Springer, Heidelberg (2011) 21. : Fpga implementation of a recently published signature scheme.
In: Comtemporary Cryptology - the Science of Information Integrity, pp. 501–540 (1992) 24. : Attaques de cryptosyst`emes ` a mots de poids faible et construction de fonctions t-r´esilientes. PhD thesis, Universit´e Paris VI (1996) 25. : A new algorithm for ﬁnding minimum-weight words in a linear code: Application to McEliece’s cryptosystem and to narrow-sense bch codes of length 511. IEEE Transactions on Information Theory 44(1), 367–378 (1998) 26. : Cryptanalysis of the original McEliece cryptosystem.
The secret to be shared is the information symbol m0 . Table 11 describes the protocol. When r users meet together, they know r symbols (and their positions) of the whole codeword c. The remaining n − r symbols are called erasures: simply replace them with 0 and they become special errors whose positions are known. Remark 8. Notice that since the protocol is used over Fq we have n = q − 1. Proposition 3. Reed-Solomon codes can polynomially decode ne errors and nε erasures provided that 2ne + nε < n − k + 1.