Now showing items 1-12 of 12

    • 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 ...
    • Design, Analysis, and Optimization of Isogeny-Based Key Establishment Protocols 

      LeGrow, Jason Travis (University of Waterloo, 2020-08-19)
      We analyze the Commutative Supersingular Isogeny Diffie-Hellman protocol (CSIDH), a novel supersingular isogeny-based key establishment protocol. Our analysis is from three perspectives: Quantum Cryptanalysis. Building ...
    • An Isogeny-Based Adaptor Signature Using SQISign 

      Gilchrist, Valerie (University of Waterloo, 2022-04-19)
      Transactions on blockchains can prove very costly, so as a solution to avoid these large costs, schemes involving payment channel networks have been developed. One approach to implementing these off-chain forms of payment ...
    • 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 ...
    • Security Analysis of Isogeny-Based Cryptosystems 

      Leonardi, Christopher (University of Waterloo, 2020-08-20)
      Let $E$ be a supersingular elliptic curve over a finite field. In this document we study public-key encryption schemes which use non-constant rational maps from $E$. The purpose of this study is to determine if such ...
    • Smoothening Functions and the Homomorphism Learning Problem 

      Ruiz Lopez, Luis A (University of Waterloo, 2020-09-02)
      This thesis is an exploration of certain algebraic and geometrical aspects of the Learning With Errors (LWE) problem introduced in Reg05. On the algebraic front, we view it as a Learning Homomorphisms with Noise problem, ...
    • User-Controlled Computations in Untrusted Computing Environments 

      Vinayagamurthy, Dhinakaran (University of Waterloo, 2019-01-15)
      Computing infrastructures are challenging and expensive to maintain. This led to the growth of cloud computing with users renting computing resources from centralized cloud providers. There is also a recent promise in ...


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