Now showing items 1-20 of 22

    • 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 ...
    • Computational Approaches to Problems in Noncommutative Algebra -- Theory, Applications and Implementations 

      Heinle, Albert (University of Waterloo, 2016-09-28)
      Noncommutative rings appear in several areas of mathematics. Most prominently, they can be used to model operator equations, such as differential or difference equations. In the Ph.D. studies leading to this thesis, ...
    • Digital Signature Schemes Based on Hash Functions 

      Lafrance, Philip (University of Waterloo, 2017-04-19)
      Cryptographers and security experts around the world have been awakened to the reality that one day (potentially soon) large-scale quantum computers may be available. Most of the public-key cryptosystems employed today on ...
    • Fast Algorithms for Finding the Characteristic Polynomial of a Rank-2 Drinfeld Module 

      Musleh, Yossef (University of Waterloo, 2018-09-21)
      This thesis introduces a new Monte Carlo randomized algorithm for computing the characteristic polynomial of a rank-2 Drinfeld module. We also introduce a deterministic algorithm that uses some ideas seen in Schoof's ...
    • Fast Bootstrapping in Z_q 

      Ruiz Lopez, Luis A (University of Waterloo, 2015-08-28)
      In 2015, Ducas and Micciancio presented a novel technique to compute the NAND gate using the Learning With Errors cryptosystem (LWE), along with a novel bootstrapping technique that turns turns this cryptosystem into a ...
    • Generic Attacks on Hash Functions 

      Upadhyay, Jalaj (University of Waterloo, 2010-09-28)
      The subject of this thesis is a security property of hash functions, called chosen-target forced-prefix preimage (CTFP) resistance and the generic attack on this property, called the herding attack. The study of CTFP ...
    • Homomorphic Encryption 

      Weir, Brandon (University of Waterloo, 2013-01-24)
      In this thesis, we provide a summary of fully homomorphic encryption, and in particular, look at the BGV encryption scheme by Brakerski, Gentry, and Vaikuntanathan; as well the DGHV encryption scheme by van Dijk, Gentry, ...
    • Implementing the Schoof-Elkies-Atkin Algorithm with NTL 

      Kok, Yik Siong (University of Waterloo, 2013-04-30)
      In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order ...
    • 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 ...
    • MAC Constructions: Security Bounds and Distinguishing Attacks 

      Mandal, Avradip (University of Waterloo, 2007-05-18)
      We provide a simple and improved security analysis of PMAC, a Parallelizable MAC (Message Authentication Code) defined over arbitrary messages. A similar kind of result was shown by Bellare, Pietrzak and Rogaway at ...
    • Message Authentication and Recognition Protocols Using Two-Channel Cryptography 

      Mashatan, Atefeh (University of Waterloo, 2008-12-02)
      We propose a formal model for non-interactive message authentication protocols (NIMAPs) using two channels and analyze all the attacks that can occur in this model. Further, we introduce the notion of hybrid-collision ...
    • Novel Secret Sharing and Commitment Schemes for Cryptographic Applications 

      Nojoumian, Mehrdad (University of Waterloo, 2012-08-15)
      In the second chapter, the notion of a social secret sharing (SSS) scheme is introduced in which shares are allocated based on a player's reputation and the way she interacts with other parties. In other words, this scheme ...
    • The Number Field Sieve for Barreto-Naehrig Curves: Smoothness of Norms 

      Shantz, Michael (University of Waterloo, 2015-05-20)
      The security of pairing-based cryptography can be reduced to the difficulty of the discrete logarithm problem (DLP) in finite fields of medium characteristic. The number field sieve is the best known algorithm for this ...
    • On the effectiveness of isogeny walks for extending cover attacks on elliptic curves 

      Yee, Randy (University of Waterloo, 2016-08-23)
      Cryptographic systems based on the elliptic curve discrete logarithm problem (ECDLP) are widely deployed in the world today. In order for such a system to guarantee a particular security level, the elliptic curve selected ...
    • On the Efficiency and Security of Cryptographic Pairings 

      Knapp, Edward (University of Waterloo, 2012-12-19)
      Pairing-based cryptography has been employed to obtain several advantageous cryptographic protocols. In particular, there exist several identity-based variants of common cryptographic schemes. The computation of a single ...
    • On the Security of Leakage Resilient Public Key Cryptography 

      Brydon, Dale (University of Waterloo, 2012-04-30)
      Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these ...
    • On the Security of Some Variants of RSA 

      Hinek, M. Jason (University of Waterloo, 2007-05-10)
      The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used public-key cryptosystem in the world today. Compared to other public-key cryptosystems, such as elliptic ...
    • Perfect Hash Families: Constructions and Applications 

      Kim, Kyung-Mi (University of Waterloo, 2003)
      Let <b>A</b> and <b>B</b> be finite sets with |<b>A</b>|=<i>n</i> and |<b>B</b>|=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)-<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> ...
    • 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 ...


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