{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T12:48:33Z","timestamp":1777985313568,"version":"3.51.4"},"reference-count":68,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,6,5]]},"abstract":"Abstract<\/jats:title>\n \n A key encapsulation mechanism (\n \n \n \n \n KEM<\/m:mi>\n <\/m:math>\n {\\mathsf{KEM}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ) that takes as input an arbitrary string, i.e., a tag, is known as tag-\n \n \n \n \n KEM<\/m:mi>\n <\/m:math>\n {\\mathsf{KEM}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , while a scheme that combines signature and encryption is called signcryption. In this article, we present a code-based signcryption tag-\n \n \n \n \n KEM<\/m:mi>\n <\/m:math>\n {\\mathsf{KEM}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n scheme. We utilize a code-based signature and an\n \n \n \n \n IND<\/m:mi>\n \n \n -<\/m:mtext>\n \n <\/m:mstyle>\n CCA2<\/m:mi>\n <\/m:math>\n {\\mathsf{IND}}\\hspace{0.1em}\\text{-}\\hspace{0.1em}{\\mathsf{CCA2}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (adaptive chosen ciphertext attack) secure version of McEliece\u2019s encryption scheme. The proposed scheme uses an equivalent subcode as a public code for the receiver, making the NP-completeness of the subcode equivalence problem be one of our main security assumptions. We then base the signcryption tag-\n \n \n \n \n KEM<\/m:mi>\n <\/m:math>\n {\\mathsf{KEM}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n to design a code-based hybrid signcryption scheme. A hybrid scheme deploys asymmetric- as well as symmetric-key encryption. We give security analyses of both our schemes in the standard model and prove that they are secure against\n \n \n \n \n IND<\/m:mi>\n \n \n -<\/m:mtext>\n \n <\/m:mstyle>\n CCA2<\/m:mi>\n <\/m:math>\n {\\mathsf{IND}}\\hspace{0.1em}\\text{-}\\hspace{0.1em}{\\mathsf{CCA2}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (indistinguishability under adaptive chosen ciphertext attack) and\n \n \n \n \n SUF<\/m:mi>\n \n \n -<\/m:mtext>\n \n <\/m:mstyle>\n CMA<\/m:mi>\n <\/m:math>\n {\\mathsf{SUF}}\\hspace{0.1em}\\text{-}\\hspace{0.1em}{\\mathsf{CMA}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (strong existential unforgeability under chosen message attack).\n <\/jats:p>","DOI":"10.1515\/jmc-2022-0002","type":"journal-article","created":{"date-parts":[[2023,6,5]],"date-time":"2023-06-05T11:41:56Z","timestamp":1685965316000},"source":"Crossref","is-referenced-by-count":0,"title":["A code-based hybrid signcryption scheme"],"prefix":"10.1515","volume":"17","author":[{"given":"Jean Belo","family":"Klamti","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Waterloo , 200 University Ave W , Waterloo , ON, N2L 3G1 , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. 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In: Practical Signcryption. Berlin, Heidelberg: Springer; 2010. p. 99\u2013117.","DOI":"10.1007\/978-3-540-89411-7_6"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_009","doi-asserted-by":"crossref","unstructured":"Sato S, Shikata J. Lattice-based signcryption without random oracles. In: Post-Quantum Cryptography: 9th International Conference, PQCrypto 2018, Fort Lauderdale, FL, USA, April 9\u201311, 2018, Proceedings. Springer; 2018. p. 331\u201351.","DOI":"10.1007\/978-3-319-79063-3_16"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_010","doi-asserted-by":"crossref","unstructured":"Yan J, Wang L, Wang L, Yang Y, Yao W. Efficient lattice-based signcryption in standard model. Math Problem Eng. 2013;2013:1\u201318.","DOI":"10.1155\/2013\/702539"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_011","doi-asserted-by":"crossref","unstructured":"Le HQ, Duong DH, Roy PS, Susilo W, Fukushima K, Kiyomoto S. Lattice-based signcryption with equality test in standard model. 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On provably secure code-based signature and signcryption scheme. IACR Cryptol ePrint Archive. 2012;2012:585."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_019","doi-asserted-by":"crossref","unstructured":"Song Y, Li Z, Li Y, Li J. Attribute-based signcryption scheme based on linear codes. Inform Sci. 2017;417:301\u20139.","DOI":"10.1016\/j.ins.2017.06.033"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_020","doi-asserted-by":"crossref","unstructured":"Banegas G, Barreto PS, Boidje BO, Cayrel PL, Dione GN, Gaj K, et al. DAGS: Key encapsulation using dyadic GS codes. J Math Cryptol. 2018;12(4):221\u201339.","DOI":"10.1515\/jmc-2018-0027"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_021","doi-asserted-by":"crossref","unstructured":"Cayrel PL, Hoffmann G, Persichetti E. Efficient implementation of a CCA2-secure variant of McEliece using generalized Srivastava codes. 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In: Post-Quantum Cryptography: 4th International Workshop, PQCrypto 2011, Taipei, Taiwan, November 29\u2013December 2, 2011. Proceedings 4. Springer; 2011. p. 51\u201367.","DOI":"10.1007\/978-3-642-25405-5_4"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_025","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re JC, Gauthier-Umana V, Otmani A, Perret L, Tillich JP. A distinguisher for high-rate McEliece cryptosystems. IEEE Trans Inform Theory. 2013;59(10):6830\u201344.","DOI":"10.1109\/TIT.2013.2272036"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_026","unstructured":"Debris-Alazard T, Sendrier N, Tillich JP. The problem with the SURF scheme. 2017. arXiv: http:\/\/arXiv.org\/abs\/arXiv:170608065."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_027","doi-asserted-by":"crossref","unstructured":"Berger TP, Gueye CT, Klamti JB. A NP-complete problem in coding theory with application to code-based cryptography. 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Cryptology ePrint Archive: Report 2018\/996; 2018. https:\/\/eprint.iacr.org\/2018\/996\/20181022:154324."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_042","unstructured":"Banegas G, Debris-Alazard T, Nedeljkovi\u0107 M, Smith B. Wavelet: Code-based postquantum signatures with fast verification on microcontrollers. 2021. arXiv: http:\/\/arXiv.org\/abs\/arXiv:211013488."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_043","doi-asserted-by":"crossref","unstructured":"Fiat A, Shamir A. How to prove yourself: Practical solutions to identification and signature problems. In: Advances in Cryptology-CRYPTO-86: Proceedings 6. Springer; 1987. p. 186\u201394.","DOI":"10.1007\/3-540-47721-7_12"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_044","doi-asserted-by":"crossref","unstructured":"Stern J. A new identification scheme based on syndrome decoding. In: Advances in Cryptology\u2013CRYPTO'93: 13th Annual International Cryptology Conference Santa Barbara, California, USA August 22\u201326, 1993 Proceedings. Springer; 1993. p. 13\u201321.","DOI":"10.1007\/3-540-48329-2_2"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_045","doi-asserted-by":"crossref","unstructured":"Jain A, Krenn S, Pietrzak K, Tentes A. Commitments and efficient zero-knowledge proofs from learning parity with noise. In: Advances in Cryptology-ASIACRYPT 2012: 18th International Conference on the Theory and Application of Cryptology and Information Security, Beijing, China, December 2\u20136, 2012. Proceedings 18. Springer; 2012. p. 663\u201380.","DOI":"10.1007\/978-3-642-34961-4_40"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_046","doi-asserted-by":"crossref","unstructured":"Cayrel PL, V\u00e9ron P, Alaoui SMEY. A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem. In: Selected areas in cryptography. vol. 6544. Berlin, Heidelberg: Springer; 2010. p. 171\u201386.","DOI":"10.1007\/978-3-642-19574-7_12"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_047","doi-asserted-by":"crossref","unstructured":"Lyubashevsky V. Fiat-Shamir with aborts: Applications to lattice and factoring-based signatures. In: Advances in Cryptology-ASIACRYPT 2009: 15th International Conference on the Theory and Application of Cryptology and Information Security, Tokyo, Japan, December 6\u201310, 2009. Proceedings 15. Springer; 2009. p. 598\u2013616.","DOI":"10.1007\/978-3-642-10366-7_35"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_048","doi-asserted-by":"crossref","unstructured":"Biasse JF, Micheli G, Persichetti E, Santini P. LESS is more: code-based signatures without syndromes. In: Progress in Cryptology-AFRICACRYPT 2020: 12th International Conference on Cryptology in Africa, Cairo, Egypt, July 20\u201322, 2020, Proceedings 12. Springer; 2020. p. 45\u201365.","DOI":"10.1007\/978-3-030-51938-4_3"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_049","doi-asserted-by":"crossref","unstructured":"Persichetti E. Efficient one-time signatures from quasi-cyclic codes: A full treatment. Cryptography. 2018;2(4):30.","DOI":"10.3390\/cryptography2040030"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_050","unstructured":"Persichetti E. Improving the efficiency of code-based cryptography. PhD thesis, University of Auckland; 2012."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_051","unstructured":"Fukushima K, Roy PS, Xu R, Kiyomoto S, Morozov K, Takagi T. Random code-based signature scheme (racoss). First round submission to the NIST post-quantum cryptography call. 2017."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_052","unstructured":"Li Z, Xing C, Yeo SL. A new code based signature scheme without trapdoors. Cryptology ePrint Archive. 2020."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_053","doi-asserted-by":"crossref","unstructured":"Song Y, Huang X, Mu Y, Wu W, Wang H. A code-based signature scheme from the Lyubashevsky framework. Theoret Comput Sci. 2020;835:15\u201330.","DOI":"10.1016\/j.tcs.2020.05.011"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_054","doi-asserted-by":"crossref","unstructured":"Aragon N, Blazy O, Gaborit P, Hauteville A, Z\u00e9mor G. Durandal: a rank metric based signature scheme. In: Advances in Cryptology-EUROCRYPT 2019: 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19\u201323, 2019, Proceedings, Part III 38. Springer; 2019. p. 728\u201358.","DOI":"10.1007\/978-3-030-17659-4_25"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_055","doi-asserted-by":"crossref","unstructured":"Debris-Alazard T, Sendrier N, Tillich JP. Wave: A new family of trapdoor one-way preimage sampleable functions based on codes. In: Advances in Cryptology-ASIACRYPT 2019: 25th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, Japan, December 8\u201312, 2019, Proceedings, Part I. Springer; 2019. p. 21\u201351.","DOI":"10.1007\/978-3-030-34578-5_2"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_056","doi-asserted-by":"crossref","unstructured":"Baek J, Steinfeld R, Zheng Y. Formal proofs for the security of signcryption. In: Public Key Cryptography: 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002 Paris, France, February 12\u201314, 2002 Proceedings 5. Springer; 2002. p. 80\u201398.","DOI":"10.1007\/3-540-45664-3_6"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_057","unstructured":"Yung M. Practical signcryption. Germany: Springer Science & Business Media; 2010."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_058","doi-asserted-by":"crossref","unstructured":"Fujisaki E, Okamoto T. Secure integration of asymmetric and symmetric encryption schemes. In: Advances in Cryptology-CRYPTO-99: 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15-19, 1999 Proceedings. Springer; 1999. p. 537\u201354.","DOI":"10.1007\/3-540-48405-1_34"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_059","doi-asserted-by":"crossref","unstructured":"Barelli E, Couvreur A. An efficient structural attack on NIST submission DAGS. In: Advances in Cryptology-ASIACRYPT 2018: 24th International Conference on the Theory and Application of Cryptology and Information Security, Brisbane, QLD, Australia, December 2\u20136, 2018, Proceedings, Part I 24. Springer; 2018. p. 93\u2013118.","DOI":"10.1007\/978-3-030-03326-2_4"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_060","doi-asserted-by":"crossref","unstructured":"Prange E. The use of information sets in decoding cyclic codes. IEEE Trans Inform Theory. 1962;8(5):5\u20139.","DOI":"10.1109\/TIT.1962.1057777"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_061","unstructured":"Bernstein DJ, Chou T, Lange T, von Maurich I, Misoczki R, Niederhagen R, et al. Classic McEliece: conservative code-based cryptography. NIST submissions. 2017."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_062","doi-asserted-by":"crossref","unstructured":"Pellikaan R, M\u00e1rquez-Corbella I. Error-correcting pairs for a public-key cryptosystem. In: Journal of Physics: Conference Series. vol. 855. IOP Publishing; 2017. p. 012032.","DOI":"10.1088\/1742-6596\/855\/1\/012032"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_063","doi-asserted-by":"crossref","unstructured":"Mora R, Tillich JP. On the dimension and structure of the square of the dual of a Goppa code. Des Codes Cryptogr. 2023;91(4):1351\u201372.","DOI":"10.1007\/s10623-022-01153-w"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_064","unstructured":"Lampe R, Patarin J. Analysis of some natural variants of the PKP algorithm. Cryptology ePrint Archive. 2011."},{"key":"2025120600280423299_j_jmc-2022-0002_ref_065","doi-asserted-by":"crossref","unstructured":"Georgiades J. Some remarks on the security of the identification scheme based on permuted kernels. J Cryptol. 1992;5:133\u20137.","DOI":"10.1007\/BF00193565"},{"key":"2025120600280423299_j_jmc-2022-0002_ref_066","doi-asserted-by":"crossref","unstructured":"Paiva TB, Terada R. Cryptanalysis of the binary permuted kernel problem. In: Applied Cryptography and Network Security: 19th International Conference, ACNS 2021, Kamakura, Japan, June 21\u201324, 2021, Proceedings, Part II. 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