We derive an explicit method of computing the composition step in Cantor\u2019s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor\u2019s general composition involves arithmetic in the polynomial ring Fq[x], the algorithm we propose solves a linear system over the base \ufb01eld which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more e\ufb03cient formulas for group operations in both a\ufb03ne and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.<\/p>\n","protected":false},"excerpt":{"rendered":"
We derive an explicit method of computing the composition step in Cantor\u2019s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor\u2019s general composition involves arithmetic in the polynomial ring Fq[x], the algorithm we […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13558],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-163875","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"Selected Areas in 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