Matches in SemOpenAlex for { <https://semopenalex.org/work/W4320154969> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W4320154969 endingPage "96" @default.
- W4320154969 startingPage "67" @default.
- W4320154969 abstract "We address three main open problems concerning the use of radical isogenies, as presented by Castryck, Decru and Vercauteren at Asiacrypt 2020, in the computation of long chains of isogenies of fixed, small degree between elliptic curves over finite fields. Firstly, we present an interpolation method for finding radical isogeny formulae in a given degree N, which by-passes the need for factoring division polynomials over large function fields. Using this method, we are able to push the range for which we have formulae at our disposal from $$N le 13$$ to $$N le 37$$ (where in the range $$18 le N le 37$$ we have restricted our attention to prime powers). Secondly, using a combination of known techniques and ad-hoc manipulations, we derive optimized versions of these formulae for $$N le 19$$ , with some instances performing more than twice as fast as their counterparts from 2020. Thirdly, we solve the problem of understanding the correct choice of radical when walking along the surface between supersingular elliptic curves over $$mathbb {F}_p$$ with $$p equiv 7 bmod 8$$ ; this is non-trivial for even N and was settled for $$N = 2$$ and $$N = 4$$ only, in the latter case by Onuki and Moriya at PKC 2022. We give a conjectural statement for all even N and prove it for $$N le 14$$ . The speed-ups obtained from these techniques are substantial: using 16-isogenies, the computation of long chains of 2-isogenies over 512-bit prime fields can be accelerated by a factor 3, and the previous implementation of CSIDH using radical isogenies can be sped up by about $$12%$$ ." @default.
- W4320154969 created "2023-02-13" @default.
- W4320154969 creator A5032574536 @default.
- W4320154969 creator A5034249182 @default.
- W4320154969 creator A5041607172 @default.
- W4320154969 creator A5061835042 @default.
- W4320154969 date "2022-01-01" @default.
- W4320154969 modified "2023-10-18" @default.
- W4320154969 title "Horizontal Racewalking Using Radical Isogenies" @default.
- W4320154969 cites W113724724 @default.
- W4320154969 cites W1508193711 @default.
- W4320154969 cites W2041753316 @default.
- W4320154969 cites W2145921801 @default.
- W4320154969 cites W2205392500 @default.
- W4320154969 cites W2595374219 @default.
- W4320154969 cites W2811492100 @default.
- W4320154969 cites W2918362961 @default.
- W4320154969 cites W2990498574 @default.
- W4320154969 cites W2991397127 @default.
- W4320154969 cites W3013936128 @default.
- W4320154969 cites W3082533815 @default.
- W4320154969 cites W3100502141 @default.
- W4320154969 cites W3171641480 @default.
- W4320154969 cites W4210397640 @default.
- W4320154969 cites W4214685745 @default.
- W4320154969 cites W4252452590 @default.
- W4320154969 cites W4254894701 @default.
- W4320154969 cites W4285272970 @default.
- W4320154969 cites W4292027090 @default.
- W4320154969 doi "https://doi.org/10.1007/978-3-031-22966-4_3" @default.
- W4320154969 hasPublicationYear "2022" @default.
- W4320154969 type Work @default.
- W4320154969 citedByCount "2" @default.
- W4320154969 countsByYear W43201549692023 @default.
- W4320154969 crossrefType "book-chapter" @default.
- W4320154969 hasAuthorship W4320154969A5032574536 @default.
- W4320154969 hasAuthorship W4320154969A5034249182 @default.
- W4320154969 hasAuthorship W4320154969A5041607172 @default.
- W4320154969 hasAuthorship W4320154969A5061835042 @default.
- W4320154969 hasConcept C11413529 @default.
- W4320154969 hasConcept C114614502 @default.
- W4320154969 hasConcept C118615104 @default.
- W4320154969 hasConcept C121332964 @default.
- W4320154969 hasConcept C159985019 @default.
- W4320154969 hasConcept C179603306 @default.
- W4320154969 hasConcept C184992742 @default.
- W4320154969 hasConcept C192562407 @default.
- W4320154969 hasConcept C202444582 @default.
- W4320154969 hasConcept C204323151 @default.
- W4320154969 hasConcept C24890656 @default.
- W4320154969 hasConcept C2775997480 @default.
- W4320154969 hasConcept C2779765290 @default.
- W4320154969 hasConcept C33923547 @default.
- W4320154969 hasConcept C45374587 @default.
- W4320154969 hasConcept C77926391 @default.
- W4320154969 hasConceptScore W4320154969C11413529 @default.
- W4320154969 hasConceptScore W4320154969C114614502 @default.
- W4320154969 hasConceptScore W4320154969C118615104 @default.
- W4320154969 hasConceptScore W4320154969C121332964 @default.
- W4320154969 hasConceptScore W4320154969C159985019 @default.
- W4320154969 hasConceptScore W4320154969C179603306 @default.
- W4320154969 hasConceptScore W4320154969C184992742 @default.
- W4320154969 hasConceptScore W4320154969C192562407 @default.
- W4320154969 hasConceptScore W4320154969C202444582 @default.
- W4320154969 hasConceptScore W4320154969C204323151 @default.
- W4320154969 hasConceptScore W4320154969C24890656 @default.
- W4320154969 hasConceptScore W4320154969C2775997480 @default.
- W4320154969 hasConceptScore W4320154969C2779765290 @default.
- W4320154969 hasConceptScore W4320154969C33923547 @default.
- W4320154969 hasConceptScore W4320154969C45374587 @default.
- W4320154969 hasConceptScore W4320154969C77926391 @default.
- W4320154969 hasLocation W43201549691 @default.
- W4320154969 hasOpenAccess W4320154969 @default.
- W4320154969 hasPrimaryLocation W43201549691 @default.
- W4320154969 hasRelatedWork W1544814744 @default.
- W4320154969 hasRelatedWork W2060770809 @default.
- W4320154969 hasRelatedWork W2086709251 @default.
- W4320154969 hasRelatedWork W2782666042 @default.
- W4320154969 hasRelatedWork W3019060828 @default.
- W4320154969 hasRelatedWork W3200844503 @default.
- W4320154969 hasRelatedWork W4225761998 @default.
- W4320154969 hasRelatedWork W4281702715 @default.
- W4320154969 hasRelatedWork W4297860324 @default.
- W4320154969 hasRelatedWork W4221148445 @default.
- W4320154969 isParatext "false" @default.
- W4320154969 isRetracted "false" @default.
- W4320154969 workType "book-chapter" @default.