Bauer, MarkHosseini Lavasani, Seyed Ahmad2016-02-242016-02-242016-02-242016Hosseini Lavasani, S. A. (2016). Classifying Hyperelliptic Trace Zero Varieties Susceptible To Low Genus Cover Attack (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25332http://hdl.handle.net/11023/2854A cover attack (on a Jacobian of a curve) is a method of decreasing the complexity of the discrete logarithm problem defined on the Jacobian of a curve by transferring it via a shared cover to the Jacobian of a new curve which admits a more efficient solution for this problem. We study different approaches that have been taken toward cover attacks and we propose new approaches for the problem of finding covers. We then concentrate on the case of cryptosystems based on the Trace Zero Variety (TZV) associated with hyperelliptic curves. We propose and implement an algorithmic solution to answer the question of finding the best cover to attack a given TZV of genus 2 curves. We extend current methods for constructing covers suitable for the attack. Subsequently, we construct all families of covers of genus 3, 4, and 5 which can potentially be used to attack such TZVs. In this way, we classify, as parametric families, all hyperelliptic curves which are vulnerable to a lower genus cover attack. As a result, we develop a method to avoid using hyperelliptic TZVs with a lower genus cover in cryptographic applications.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Education--MathematicsCryptographyCover attackTrace Zero VarietyHyperelliptic curvesdoctoral thesishttp://dx.doi.org/10.11575/PRISM/25332