Construction of Secure Cab Curves Using Modular Curves
This paper proposes an algorithm which, given a basis of a subspace of the space of cuspforms of weight 2 for Γ0(N) which is invariant for the action of the Hecke operators, tests whether the subspace corresponds to a quotient A of the jacobian of the modular curve X 0(N) such that A is the jacobian of a curve C. Moreover, equations for such a curve C are computed which make the quotient suitable for applications in cryptography. One advantage of using such quotients of modular jacobians is that fast methods are known for finding their number of points over finite fields . Our results extend ideas of M. Shimura  who used only the full modular jacobian instead of abelian quotients of it.
KeywordsErential Form Algebraic Curve Hyperelliptic Curve Weierstrass Point Modular Curve
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