Browsing University of Waterloo by Supervisor "Jao, David"
Now showing items 1-12 of 12
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Abstract and Explicit Constructions of Jacobian Varieties
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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 ...