Formulae for arithmetic on genus 2 hyperelliptic curves

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    77 Citaten (Scopus)

    Samenvatting

    The ideal class group of hyperelliptic curves can be used in cryptosystems based on the discrete logarithm problem. In this article we present explicit formulae to perform the group operations for genus 2 curves. The formulae are completely general but to achieve the lowest number of operations we treat odd and even characteristic separately. We present 3 different coordinate systems which are suitable for different environments, e. g. on a smart card we should avoid inversions while in software a limited number is acceptable. The presented formulae render genus two hyperelliptic curves very useful in practice. The first system are affine coordinates where each group operation needs one inversion. Then we consider projective coordinates avoiding inversions on the cost of more multiplications and a further coordinate. Finally, we introduce a new system of coordinates and state algorithms showing that doublings are comparably cheap and no inversions are needed. A comparison between the systems concludes the paper.
    Originele taal-2Engels
    Pagina's (van-tot)295-328
    TijdschriftApplicable Algebra in Engineering, Communication and Computing
    Volume15
    Nummer van het tijdschrift5
    DOI's
    StatusGepubliceerd - 2005

    Vingerafdruk

    Duik in de onderzoeksthema's van 'Formulae for arithmetic on genus 2 hyperelliptic curves'. Samen vormen ze een unieke vingerafdruk.

    Citeer dit