International Association for Cryptologic Research

Ph.D. Database

The aim of the IACR Ph.D. database is twofold. On the first hand, we want to offer an overview of Ph.D. already completed in the domain of cryptology. Where possible, this should also include a subject classification, an abstract, and access to the full text. On the second hand, it deals with Ph.D. subjects currently under investigation. This way, we provide a timely map of contemporary research in cryptology. All entries or changes need to be approved by an editor. You can contact them via phds (at)


Eric Bone (#551)
Name Eric Bone
Institution Brandeis University
Topic of his/her doctorate. A Generalization of Pohlig-Hellman Simplification in Elliptic Curve Cryptography
Category public-key cryptography
Keywords elliptic curve cryptosystem
Ph.D. Supervisor(s) Fred Diamond
Year of completion 2004
Abstract Let E be an elliptic curve over F_p. We investigate the construction of elliptic curve cryptosystems which use a commutative subring S of End(E), which is strictly larger than Z. Elliptic curve cryptosystems can be constructed based on the difficulty of solving this problem. We formulate a Generalized Elliptic Curve Discrete Logarithm Problem as follows: given a point P in E(F_p^r) and Q in the S-module generated by P, find a map Psi in S such that Q=Psi(P). Let Frob be the p-th power Frobenius map. We display a generalization of Pohlig-Hellman simplification to the case where S= Z[Frob] = End(E). We write S/ann(P) as a product of local rings. Then we show how to solve for the projection of Psi in each local ring by solving a series of congruences modulo the annihilators of progressively smaller powers of the maximal ideal. The most interesting cases are those where the maximal ideal is not principal.
E-Mail Address ithambo (at)
Last Change 2011-05-14 23:40:13
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