Browsing by Author "LeGrow, Jason Travis"

Now showing 1 - 2 of 2
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    Deciding if a Genus 1 Curve has a Rational Point
    Swanson, Nicolas J. Brennan (Virginia Tech, 2024-05-23)
    Many sources suggest a folklore procedure to determine if a smooth curve of genus 1 has a rational point. This procedure terminates conditionally on the Tate-Shafarevich conjecture. In this thesis, we provide an exposition for this procedure, making several steps explicit. In some instances, we also provide MAGMA implementations of the subroutines. In particular, we give an algorithm to determine if a smooth, genus 1 curve of arbitrary degree is locally soluble, we compute its Jacobian, and we give an exposition for descent in our context. Additionally, we prove there exists an algorithm to decide if smooth, genus 1 curve has a rational point if and only if there exists an algorithm to compute the Mordeil-Weil group of an elliptic curve.
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    Fault Injection Attacks on RSA and CSIDH
    Chiu, TingHung (Virginia Tech, 2024-05-16)
    Fault injection attacks are a powerful technique that intentionally induces faults during computations to leak secret information. This thesis studies the fault injection attack techniques. The thesis first categorizes various fault attack methods by fault model and fault analysis and gives examples of the various fault attacks on symmetric key cryptosystems and public key cryptosystems. The thesis then demonstrates fault injection attacks on RSA-CRT and constant time CSIDH. The fault attack consists of two main components: fault modeling, which examines methods for injecting faults in a target device, and fault analysis, which analyzes the resulting faulty outputs to deduce secrets in each cryptosystem. The thesis aims to provide a comprehensive survey on fault attack research, directions for further study on securing real-world cryptosystems against fault injection attacks, testing fault injection attacks with RSA-CRT, and demonstrate and evaluate fault injection attacks on constant time CSIDH.