On the construction of a semantically secure modification of the McEliece cryptosystem | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 45. DOI: 10.17223/20710410/45/4

The security of currently used asymmetric cryptosystems is based on the problems of discrete logarithm or discrete factorization. These problems can be effectively solved using Shor's algorithm on quantum computers. An alternative to such cryptosystems can be the McEliece cryptosystem. Its security is based on the problem of decoding a general linear code. In its original form, the McEliece cryptosystem is not semantically secure, from here the problem of constructing a semantically secure cryptosystem of the McEliece type is relevant. In the paper, the goal is to construct a McEliece type cryptosystem that has the IND-CPA property. Further, one can suppose that this system can be used as base cryptosystem for building the McEliece type encryption scheme with the IND-CCA2 property and an efficient information transfer rate.
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  • Title On the construction of a semantically secure modification of the McEliece cryptosystem
  • Headline On the construction of a semantically secure modification of the McEliece cryptosystem
  • Publesher Tomask State UniversityTomsk State University
  • Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 45
  • Date:
  • DOI 10.17223/20710410/45/4
Keywords
McEliece type cryptosystems, IND-CPA, semantic security, standart model, криптосистемы типа Мак-Элиса, IND-CPA-свойство, семантическая стойкость
Authors
References
Kobara K. and Imai H. Semantically secure McEliece public-key cryptosystems - conversions for McEliece PKC. LNCS, 2001, vol. 1992, pp. 19-35
Goldwasser S. and Micali S. Probabilistic encryption. J. Computer and System Sciences, 1984, vol. 38, no. 2, pp. 270-299
Bellare M. and Rogaway P. Optimal asymmetric encryption - how to encrypt with RSA. Advances in Cryptology - EUROCRYPT'94, Springer Verlag, 1995, pp. 92-111
Shor P. Algorithms for quantum computation: discrete logarithms and factoring. Proc. 35th Ann. Symp. FCS, Santa Fe, USA, IEEE Publ., 1994, pp. 124-134
McEliece R. J. A public-key cryptosystem based on algebraic coding theory. DSN Progress Report, 1978, vol. 42, no. 44, pp. 114-116
Bellare M. and Rogaway P. Random oracles are practical: A paradigm for designing efficient protocols. CCS '93 Proc. 1st ACM conf. CCS'93, N.Y., ACM, 1993, pp. 62-73
Nojima R., Imai H., Kobara K., and Morozov K. Semantic security for the McEliece cryptosystem without random oracles. Designs, Codes and Cryptography, 2008, vol. 49, no. 1-3, pp. 289-305
Dottling N., Dowsley R., Muller-Quade J., and Nascimento C. A. A. A CCA2 secure variant of the McEliece cryptosystem. IEEE Trans. Inform. Theory, 2012, vol. 58, no. 10, pp. 6672-6680
Lenstra A. K. and Verheul E. R. Selecting cryptographic key sizes. J. Cryptology, 2001, vol. 14, no. 4, pp. 255-293
Bellare M., Desai A., Pointcheval D., and Rogaway P. Relations among notions of security for public-key encryption schemes. Advances in Cryptology - CRYPTO'98, LNCS, 1998, vol. 1462, pp. 26-45
Bleichenbacher D. Chosen ciphertext attacks against protocols based on the RSA encryption standard PKCS#1. Advances in Cryptology - CRYPTO'98, LNCS, 1998, vol. 1462, pp. 255-293
Cramer R., Damgard I., and Nielsen J. B. Secure Multiparty Computation and Secret Sharing. Cambridge, Cambridge University Press, 2015. 373p
Kosolapov Y. V. and Turchenko O. Y. Primenenie odnogo metoda raspoznavaniya koda dlya kanala s podslushivaniem [Application of one method of linear code recognition to the wiretap channel]. Prikladnaya Diskretnaya Matematika, 2017, no. 35, pp. 76-88. (in Russian)
Chabot C. Recognition of a code in a noisy environment. Proc. IEEE ISIT, Nice, France, 2007, pp.2211-2215.
Yardi A. D. and Vijayakumaran S. Detecting linear block codes in noise using the GLRT. IEEE Intern. Conf. Communications, Budapest, Hungary, 2013, pp. 4895-4899.
 On the construction of a semantically secure modification of the McEliece cryptosystem | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 45. DOI: 10.17223/20710410/45/4
On the construction of a semantically secure modification of the McEliece cryptosystem | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 45. DOI: 10.17223/20710410/45/4
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