Mordell's equation in characteristic three

Pairing in Characteristic Three

Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the ηT pairing in characteristic three and suggest further impr...

Characteristic Surface Data for the Eikonal Equation

A method of solving the eikonal equation, in either flat or curved space-times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front si...

Characteristic Strichartz Estimates for the Wave Equation

Integral Equation Analysis with Characteristic Basis Functions

Efficient multiplication in characteristic three fields

Characteristic three fields denoted by F3n , where n ≥ 1, are used in curve based cryptography. In this paper, first we improve the well known Karatsuba 2-way and 3-way algorithms for characteristic three fields. Then, we derive a 3-way polynomial multiplication algorithm with five 1/3 size multiplications using interpolation in F9. After computing the arithmetic and delay complexities of the p...