{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T14:17:26Z","timestamp":1772893046578,"version":"3.50.1"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,3,20]],"date-time":"2019-03-20T00:00:00Z","timestamp":1553040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>A new class of public key agreement (PKA) algorithms called strongly-asymmetric algorithms (SAA) was introduced in a previous paper by some of the present authors. This class can be shown to include some of the best-known PKA algorithms, for example the Diffie\u2013Hellman and several of its variants. In this paper, we construct a new version of the previous construction, called SAA-5, improving it in several points, as explained in the Introduction. In particular, the construction complexity is reduced, and at the same time, robustness is increased. Intuitively, the main difference between SAA-5 and the usual PKA consists of the fact that in the former class, B (Bob) has more than one public key and A (Alice) uses some of them to produce her public key and others to produce the secret shared key (SSK). This introduces an asymmetry between the sender of the message (B) and the receiver (A) and motivates the name for this class of algorithms. After describing the main steps of SAA-5, we discuss its breaking complexity assuming zero complexity of discrete logarithms and the computational complexity for both A and B to create SSK.<\/jats:p>","DOI":"10.3390\/cryptography3010009","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T04:11:56Z","timestamp":1553141516000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Class of Strongly Asymmetric PKA Algorithms: SAA-5"],"prefix":"10.3390","volume":"3","author":[{"given":"Luigi","family":"Accardi","sequence":"first","affiliation":[{"name":"Centro Vito Volterra, Via Columbia, 2, 00133 Roma, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2803-7783","authenticated-orcid":false,"given":"Satoshi","family":"Iriyama","sequence":"additional","affiliation":[{"name":"Department of Information Science, Tokyo University of Science, Yamazaki 2641, Japan"}]},{"given":"Koki","family":"Jimbo","sequence":"additional","affiliation":[{"name":"Department of Information Science, Tokyo University of Science, Yamazaki 2641, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4783-6468","authenticated-orcid":false,"given":"Massimo","family":"Regoli","sequence":"additional","affiliation":[{"name":"DICII, Engineering Faculty Via del Politecnico, Universit\u00e1 di Roma Tor Vergata, 1, 00133 Roma, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","article-title":"New directions in cryptography","volume":"22","author":"Diffie","year":"1976","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1145\/359340.359342","article-title":"A method for obtaining digital signatures and public key cryptosystems","volume":"21","author":"Rivest","year":"1978","journal-title":"Commun. ACM"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Adrian, D., Bhargavan, K., Durumeric, Z., Gaudry, P., Green, M., Halderman, J.A., Heninger, N., Springall, D., Thome, E., and Valenta, L. (2015, January 12\u201316). Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice. Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA.","DOI":"10.1145\/2810103.2813707"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Patarin, J. (1996, January 12\u201316). Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. 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