Now showing items 1-7 of 7

    • Abstract and Explicit Constructions of Jacobian Varieties 

      Urbanik, David (University of Waterloo, 2018-08-10)
      Abelian varieties, in particular Jacobian varieties, have long attracted interest in mathematics. Their influence pervades arithmetic geometry and number theory, and understanding their construction was a primary motivator ...
    • Combinatorial Arithmetic on Elliptic Curves 

      Gauthier-Shalom, Gabriel (University of Waterloo, 2017-09-27)
      We propose a scalar multiplication technique on an elliptic curve, which operates on triples of collinear points. The computation of this operation requires a new approach to operation chains, with similarities to Montgomery ...
    • Key Compression for Isogeny-Based Cryptosystems 

      Leonardi, Christopher (University of Waterloo, 2016-04-21)
      We present a method for key compression in quantum-resistant isogeny-based cryptosystems, which reduces storage and transmission costs of per-party public information by a factor of two, with no effect on the security level ...
    • A post-quantum digital signature scheme based on supersingular isogenies 

      Yoo, Youngho (University of Waterloo, 2017-09-20)
      We present the first general-purpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is ...
    • Post-Quantum Elliptic Curve Cryptography 

      Soukharev, Vladimir (University of Waterloo, 2016-05-16)
      We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These ...
    • Post-Quantum Security of Authenticated Key Establishment Protocols 

      LeGrow, Jason (University of Waterloo, 2016-04-20)
      We present a security model for authenticated key establishment that allows for quantum interactions between the adversary and quantum oracles that emulate classical parties, resulting in a truly post-quantum security ...
    • Privately Constrained Testable Pseudorandom Functions 

      Pawlega, Filip (University of Waterloo, 2018-09-20)
      Privately Constrained Pseudorandom Functions allow a PRF key to be delegated to some evaluator in a constrained manner, such that the key’s functionality is restricted with respect to some secret predicate. Variants of ...

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