Constructive and destructive facets of torus-based cryptography
نویسنده
چکیده
We introduce a constructive model for algebraic tori based on reduced divisors on singular curves. By using a singular hyperelliptic model, this provides an alternative representation, and computational model, for groups of rational points on an algebraic tori [4]. We obtain a represention of elements on certain tori of dimension r in compact representation using r +1 elements. By embedding the ElGamal discrete logarithm of a composite degree field in an algebraic torus, we obtain an attack on the discrete logarithm problem based on index calculus in the generalized Jacobian of a hyperelliptic curve.
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