Browsing by Author "LeGrow, Jason T."

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    Linear Exact Repair Schemes for Distributed Storage and Secure Distributed Matrix Multiplication
    Valvo, Daniel William (Virginia Tech, 2023-05-08)
    In this thesis we develop exact repair schemes capable of repairing or circumventing unavailable servers of a distributed network in the context of distributed storage and secure distributed matrix multiplication. We develop the (Λ, Γ, W, ⊙)-exact repair scheme framework for discussing both of these contexts and develop a multitude of explicit exact repair schemes utilizing decreasing monomial-Cartesian codes (DMC codes). Specifically, we construct novel DMC codes in the form of augmented Cartesian codes and rectangular monomial-Cartesian codes, as well as design exact repair schemes utilizing these constructions inspired by the schemes from Guruswami and Wootters [16] and Chen and Zhang [6]. In the context of distributed storage we demonstrate the existence of both high rate and low bandwidth systems based on these schemes, and we develop two methods to extend them to the l-erasure case. Additionally, we develop a family of hybrid schemes capable of attaining high rates, low bandwidths, and a balance in between which proves to be competitive compared to existing schemes. In the context of secure distributed matrix multiplication we develop similarly impactful schemes which have very competitive communication costs. We also construct an encoding algorithm based on multivariate interpolation and prove it is T-secure.
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    A Survey on Exotic Signatures for Post-Quantum Blockchain: Challenges & Research Directions
    Buser, Maxime; Dowsley, Rafael; Esgin, Muhammed; Gritti, Clementine; Kasra Kermanshahi, Shabnam; Kuchta, Veronika; LeGrow, Jason T.; Liu, Joseph; Phan, Raphaël C.-W.; Sakzad, Amin; Steinfeld, Ron; Yu, Jiangshan (ACM, 2023)
    Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this paper, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and which are crucial cryptographic tools used in the blockchain ecosystem for (i) account management, (ii) consensus efficiency, (iii) empowering scriptless blockchain, and (iv) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind and ring signatures. Herein the term exotic refers to signatures with properties which are not just beyond the norm for signatures e.g. unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats.