Affiliations: Warsaw School of Economics, Aleja Niepodległości 162, 02-554 Warsaw, Poland. [email protected]
Correspondence:
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Address for correspondence: Warsaw School of Economics, Aleja Niepodległości 162, 02-554 Warsaw, Poland.
Abstract: Formulas for doubling, differential addition and point recovery after compression were given for many standard models of elliptic curves, and allow for scalar multiplication after compression using the Montgomery ladder algorithm and point recovery on a curve after this multiplication. In this paper we give such formulas for the twisted Jacobi intersection au2 + v2 = 1, bu2 + w2 = 1. To our knowledge such formulas were not given for this model or for the Jacobi intersection. In projective coordinates these formulas have cost 2M +2S +6D for doubling and 5M + 2S + 6D for differential addition, where M; S; D are multiplication, squaring and multiplication by constants in a field, respectively, choosing suitable curve parameters cost of D may be small.
Keywords: elliptic curve cryptography, point compression on elliptic curves, the Montgomery ladder algorithm, the twisted Jacobi intersection
