{"id":2661,"date":"2025-07-26T19:56:54","date_gmt":"2025-07-26T19:56:54","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2661"},"modified":"2026-01-26T20:03:33","modified_gmt":"2026-01-26T20:03:33","slug":"a-new-public-key-encryption-scheme-based-on-the-cubic-pell-curve-using-encoding-functions","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/a-new-public-key-encryption-scheme-based-on-the-cubic-pell-curve-using-encoding-functions\/","title":{"rendered":"A New Public Key Encryption Scheme Based on the Cubic Pell Curve Using Encoding Functions"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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A New Public Key Encryption Scheme Based on the Cubic Pell Curve
Using Encoding Functions<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Abderrahmane Nitaj<\/strong>\\,^1<\/span><\/i> and Michel Seck\\,^2<\/span>
\\,^{1}<\/span>Normandie Univ, UNICAEN, CNRS, LMNO, 14000 Caen, France
\\,^{2}<\/span>Ecole Polytechnique de Thies, LTISI, Senegal.
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Pages 90-108 | Received 20 October 2024, Accepted 19 December 2024, Published 10 July 2025 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

RSA is a public key encryption scheme introduced by Rivest, Shamir, and Adleman in 1978. Its security relies on the difficulty of factoring an integer N=pq<\/span> which is the product of two large prime numbers p<\/span> and q<\/span>. In 2018, Murru and Saettone proposed a variant of RSA, based on the cubic Pell curve with a modulus of the same form. Recently, Seck and Nitaj extended the scheme of Murru and Saettone to a prime power modulus of the form N=p^rq^s<\/span> where the ciphertexts C<\/span> are represented as elements of \\mathbb{Z}\/N\\mathbb{Z}\\times \\mathbb{Z}\/N\\mathbb{Z} \\times \\mathbb{Z}\/N\\mathbb{Z}<\/span>, with a size of 3\\log_2(N)<\/span>. In addition to the difficulty of factoring composite integers, the security of the scheme of Seck and Nitaj is based on Rabin’s trapdoor one-way function. In this paper, we propose a new variant of the scheme of Seck and Nitaj where the ciphertext size is reduced to a size 2\\log_2(N)<\/span> instead of 3\\log_2(N)<\/span> for a fixed modulus N<\/span>. This achievement is made possible through the incorporation of encoding and compression functions.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span> Public Key Cryptography, cubic Pell curve, RSA variants, Encoding functions.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 94A60.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles A New Public Key Encryption Scheme Based on the Cubic Pell Curve Using Encoding Functions Abderrahmane Nitaj and Michel Seck Normandie Univ, UNICAEN, CNRS, LMNO, 14000 Caen, France Ecole Polytechnique de Thies, LTISI, Senegal. Pages 90-108 | Received 20 October 2024, Accepted 19 December 2024, Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2661","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2661","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2661"}],"version-history":[{"count":6,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2661\/revisions"}],"predecessor-version":[{"id":3022,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2661\/revisions\/3022"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}