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A New Public-Key Cryptosystem Based on LCD Codes

Year 2021, Issue: 28, 320 - 324, 30.11.2021
https://doi.org/10.31590/ejosat.999112

Abstract

A cryptosystem is a structure or scheme consisting of a set of algorithms that converts plaintext to ciphertext to encode or decode messages securely. The cryptosystem points at a computer system that employs cryptography. Cryptosystems are classified by the method they use to encrypt data. One of them is symmetric key encryption. While the symmetric key algorithm uses the same key for encryption and decryption, asymmetric key encryption or public-key encryption uses the different keys. So it is more reliable than symmetric cipher algorithm. In this paper, we propose a new public-key cryptosystem by using LCD codes and explain the signature protocol based on this system which is reliable.

References

  • Alahmadi, A., Altassan, A., AlKenani, A., Çalkavur, S., Shoaib, H., Solé, P., (2020), A Multisecret-Sharing Scheme Based on LCD Codes, Mathematics, vol. 8, no. 272.
  • Baldi, M., Bodrato, M., and Chiaraluce, F., (2008), A new analysis of the mceliece cryptosystem based on qc-ldpc codes, In Security and Cryptography for Networks, pp. 246-262, Springer.
  • Berger, T. P., and Loidreau, P., (2005), How to mask the structure of codes for a cryptographic use. Designs, Codes and Cryptography, vol. 35, no. 1, pp. 63-79.
  • Berger, T. P., Cayrel, P. -L., Gaborit, P. , and Otmani, A., (2009), Reducing key length of the mceliece cryptosystem. In Progress in Cryptology-AFRICACRYPT 2009, pp. 77-97, Springer.
  • Berlekamp, E., McEliece, R., and Tilborg, H. van, (1978), On the inherent intractability of certain coding problems (corresp.), IEEE Transactions on Information Theory, vol. 24, no. 3, pp. 384-386, May.
  • Carlet, C. , Guilley, S., (2014), Complementary dual codes for counter measures to side-channel attacks, In Proceedings of the 4th ICMCTA Meeting, Palmela, Portugal, 15-18 September 2014.
  • Dougherty, S. T. , Kim, J. -L., Özkaya, B., Solé, P., (2017), The combinatorics of LCD codes: Linear programming bound and orthogonal matrices, IJICOT 2017, vol. 4, pp. 116-128.
  • Diffie, W., and Hellman, (1976), M. E., New Directions in Cryptography, IEEE Transactions on Information Theory, IT-22, no. 6, pp.644-654, November 1976.
  • Esmaeili, M., Yari, S., (2009), On complementary-dual quasi-cyclic codes, Finite Fields Appl., vol. 15, pp. 357-386.
  • Güneri, C., Özkaya, B., Solé, P., (2016), Quasi-cyclic complementary dual codes, Finite Fields Appl., vol. 42, pp. 67-80.
  • Janwa, H., and Moreno, O., (1996), McEliece public key cryptosystems using algebraic-geometric codes, Designs, Codes and Cryptography, vol. 8, no. 3, pp. 293-307.
  • Kabatiansky, G. , Semenov, S. and Krouk, E., (2005), Error-Correcting Coding and Security for Data Networks: Analysis of the Superchannel Concept, John Wiley, Sons, p. 278.
  • Krouk, E., (1983), A New Public-Key Cryptosystem, in Sixth Joint Swedish-Russian International Workshop on Information Theory, Moelle, Sweden, pp. 285-286.
  • Krouk, E., Ovchinnikov, A., and Vostokova, E., (2016), About one modification of McEliece cryptosystem based on Plotkin construction, in 2016 XV International Symposium Problems of Redundancy in Information and Control Systems (REDUNDANCY), pp. 75-78, September 2016.
  • Krouk, E., Ovchinnikov, A., (2017), Code-Based Public-Key Cryptosystem Based on Bursts-Correcting Codes, AICT 2017, The Thirteenth Advanced International Conference on Telecommunications, pp. 93-95, IARIA.
  • Krouk, E., and Serger, U., (1998), A Public Key Cryptosystem Based on Total Decoding of Linear Codes, in VI International Workshop "Algebraic and combinatorial coding theory", Pskov, pp. 116-118.
  • Löndahl, C., and Johansson, T., (2012), A new version of mceliece pkc based on convolutional codes, In Information and Communications Security, pp. 461-470, Springer.
  • MacWilliams, F., and Sloane, N., (1983), The Theory of Error-Correcting Codes, North-Holland publishing company, p. 782.
  • Massey, J. L., (1992), Linear codes with complementary duals, Discrete Math. 106/107, pp. 337-342.
  • Massey, J. L., (1994), Reversible codes, Inf. Control, vol. 7, pp. 369-380.
  • McEliece, R. J., (1978), A Public-Key Cryptosystem Based on Algebraic Coding Theory, 1978 DSN progress report, pp. 42-44, Jet Propulsion Labaratory, Pasadena, California.
  • Misoczki, R., Tillich, J. -P. , Sendrier, N., and Barreto, P., (2013), MDPC-McEliece: New McEliece variants from moderate density parity-check codes. In Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on, pp. 2069-2073, IEEE.
  • Misoczki, R., and Barreto, P., (2009), Compact mceliece keys from goppa codes, In Selected Areas in Cryptography, pp. 376-392, Springer.
  • Ngo, X. T., Bhasin, S., Danger, J. L., Guilley, S. , Najm, S., (2015), Linear Complementary Dual Code Improvement to Strengthen Encoded Circuit Against Hardware Trojan Horses, In Proceedings of the 2015 IEEE International Symposium on Hardware Oriented Security and Trust (HOST), Washington, DC, USA, 5-7 May 2015.
  • Niederreiter, H., (1986), Knapsack-type cryptosystems and algebraic coding theory, Prob. Control and Information Theory, vol. 15, no. 2, pp. 159-166.
  • Rivest, R. L. , Shamir, A., Adleman, L., (1978), A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, https://doi.org/10.1145/359340.359342.
  • Sendrier, N., (2004), Linear codes with complementary duals meet the Gilbert-Varshamov bound, Discrete Math., vol. 285, pp. 345-347.
  • Sidelnikov, V. M., and Shestakov, S. O., (1992), On insecurity of cryptosystems based on generalized Reed-Solomon codes, Discrete Mathematics and Applications, vol. 2, no. 4, pp. 439-444.
  • Sidelnikov, V. M., (1994), A public-key cryptosystem based on binary reed-muller codes, Discrete Mathematics and Applications, vol. 4, no. 3, pp. 191-208.
  • Wang, Y., (2016), Quantum Resistant Random Linear Code Based Public Key Encryption Scheme RLCE, 2016 IEEE International Symposium on Information Theory (ISIT), DOI:10.1109/ISIT.2016.7541753, Barcelona, Spain.
  • Yang, X., Massey, J. L., (1994), The condition for a cyclic code to have a complementary duals meet the Gilbert-Varshamov bound, Discrete Math., vol. 126, pp. 391-393.

A New Public-Key Cryptosystem Based on LCD Codes

Year 2021, Issue: 28, 320 - 324, 30.11.2021
https://doi.org/10.31590/ejosat.999112

Abstract

A cryptosystem is a structure or scheme consisting of a set of algorithms that converts plaintext to ciphertext to encode or decode messages securely. The cryptosystem points at a computer system that employs cryptography. Cryptosystems are classified by the method they use to encrypt data. One of them is symmetric key encryption. While the symmetric key algorithm uses the same key for encryption and decryption, asymmetric key encryption or public-key encryption uses the different keys. So it is more reliable than symmetric cipher algorithm. In this paper, we propose a new public-key cryptosystem by using LCD codes and explain the signature protocol based on this system which is reliable.

References

  • Alahmadi, A., Altassan, A., AlKenani, A., Çalkavur, S., Shoaib, H., Solé, P., (2020), A Multisecret-Sharing Scheme Based on LCD Codes, Mathematics, vol. 8, no. 272.
  • Baldi, M., Bodrato, M., and Chiaraluce, F., (2008), A new analysis of the mceliece cryptosystem based on qc-ldpc codes, In Security and Cryptography for Networks, pp. 246-262, Springer.
  • Berger, T. P., and Loidreau, P., (2005), How to mask the structure of codes for a cryptographic use. Designs, Codes and Cryptography, vol. 35, no. 1, pp. 63-79.
  • Berger, T. P., Cayrel, P. -L., Gaborit, P. , and Otmani, A., (2009), Reducing key length of the mceliece cryptosystem. In Progress in Cryptology-AFRICACRYPT 2009, pp. 77-97, Springer.
  • Berlekamp, E., McEliece, R., and Tilborg, H. van, (1978), On the inherent intractability of certain coding problems (corresp.), IEEE Transactions on Information Theory, vol. 24, no. 3, pp. 384-386, May.
  • Carlet, C. , Guilley, S., (2014), Complementary dual codes for counter measures to side-channel attacks, In Proceedings of the 4th ICMCTA Meeting, Palmela, Portugal, 15-18 September 2014.
  • Dougherty, S. T. , Kim, J. -L., Özkaya, B., Solé, P., (2017), The combinatorics of LCD codes: Linear programming bound and orthogonal matrices, IJICOT 2017, vol. 4, pp. 116-128.
  • Diffie, W., and Hellman, (1976), M. E., New Directions in Cryptography, IEEE Transactions on Information Theory, IT-22, no. 6, pp.644-654, November 1976.
  • Esmaeili, M., Yari, S., (2009), On complementary-dual quasi-cyclic codes, Finite Fields Appl., vol. 15, pp. 357-386.
  • Güneri, C., Özkaya, B., Solé, P., (2016), Quasi-cyclic complementary dual codes, Finite Fields Appl., vol. 42, pp. 67-80.
  • Janwa, H., and Moreno, O., (1996), McEliece public key cryptosystems using algebraic-geometric codes, Designs, Codes and Cryptography, vol. 8, no. 3, pp. 293-307.
  • Kabatiansky, G. , Semenov, S. and Krouk, E., (2005), Error-Correcting Coding and Security for Data Networks: Analysis of the Superchannel Concept, John Wiley, Sons, p. 278.
  • Krouk, E., (1983), A New Public-Key Cryptosystem, in Sixth Joint Swedish-Russian International Workshop on Information Theory, Moelle, Sweden, pp. 285-286.
  • Krouk, E., Ovchinnikov, A., and Vostokova, E., (2016), About one modification of McEliece cryptosystem based on Plotkin construction, in 2016 XV International Symposium Problems of Redundancy in Information and Control Systems (REDUNDANCY), pp. 75-78, September 2016.
  • Krouk, E., Ovchinnikov, A., (2017), Code-Based Public-Key Cryptosystem Based on Bursts-Correcting Codes, AICT 2017, The Thirteenth Advanced International Conference on Telecommunications, pp. 93-95, IARIA.
  • Krouk, E., and Serger, U., (1998), A Public Key Cryptosystem Based on Total Decoding of Linear Codes, in VI International Workshop "Algebraic and combinatorial coding theory", Pskov, pp. 116-118.
  • Löndahl, C., and Johansson, T., (2012), A new version of mceliece pkc based on convolutional codes, In Information and Communications Security, pp. 461-470, Springer.
  • MacWilliams, F., and Sloane, N., (1983), The Theory of Error-Correcting Codes, North-Holland publishing company, p. 782.
  • Massey, J. L., (1992), Linear codes with complementary duals, Discrete Math. 106/107, pp. 337-342.
  • Massey, J. L., (1994), Reversible codes, Inf. Control, vol. 7, pp. 369-380.
  • McEliece, R. J., (1978), A Public-Key Cryptosystem Based on Algebraic Coding Theory, 1978 DSN progress report, pp. 42-44, Jet Propulsion Labaratory, Pasadena, California.
  • Misoczki, R., Tillich, J. -P. , Sendrier, N., and Barreto, P., (2013), MDPC-McEliece: New McEliece variants from moderate density parity-check codes. In Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on, pp. 2069-2073, IEEE.
  • Misoczki, R., and Barreto, P., (2009), Compact mceliece keys from goppa codes, In Selected Areas in Cryptography, pp. 376-392, Springer.
  • Ngo, X. T., Bhasin, S., Danger, J. L., Guilley, S. , Najm, S., (2015), Linear Complementary Dual Code Improvement to Strengthen Encoded Circuit Against Hardware Trojan Horses, In Proceedings of the 2015 IEEE International Symposium on Hardware Oriented Security and Trust (HOST), Washington, DC, USA, 5-7 May 2015.
  • Niederreiter, H., (1986), Knapsack-type cryptosystems and algebraic coding theory, Prob. Control and Information Theory, vol. 15, no. 2, pp. 159-166.
  • Rivest, R. L. , Shamir, A., Adleman, L., (1978), A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, https://doi.org/10.1145/359340.359342.
  • Sendrier, N., (2004), Linear codes with complementary duals meet the Gilbert-Varshamov bound, Discrete Math., vol. 285, pp. 345-347.
  • Sidelnikov, V. M., and Shestakov, S. O., (1992), On insecurity of cryptosystems based on generalized Reed-Solomon codes, Discrete Mathematics and Applications, vol. 2, no. 4, pp. 439-444.
  • Sidelnikov, V. M., (1994), A public-key cryptosystem based on binary reed-muller codes, Discrete Mathematics and Applications, vol. 4, no. 3, pp. 191-208.
  • Wang, Y., (2016), Quantum Resistant Random Linear Code Based Public Key Encryption Scheme RLCE, 2016 IEEE International Symposium on Information Theory (ISIT), DOI:10.1109/ISIT.2016.7541753, Barcelona, Spain.
  • Yang, X., Massey, J. L., (1994), The condition for a cyclic code to have a complementary duals meet the Gilbert-Varshamov bound, Discrete Math., vol. 126, pp. 391-393.
There are 31 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Selda Çalkavur 0000-0002-1502-123X

Publication Date November 30, 2021
Published in Issue Year 2021 Issue: 28

Cite

APA Çalkavur, S. (2021). A New Public-Key Cryptosystem Based on LCD Codes. Avrupa Bilim Ve Teknoloji Dergisi(28), 320-324. https://doi.org/10.31590/ejosat.999112