الفهرس 
Powers and Primitive Roots in Finite Fields
Error Analysis and Detection Procedures for Elliptic Curve Digital Signature AlgorithmOnly 14 pages are availabe for public view
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Abstract
Traditional mathematical cryptanalysis uncovers weakness in cryptographic algorithms. A small amount of side-channel information is sufficient to compromise common cryptographic algorithms. We added new modifications to some cryptographic techniques to improve their security and reliability in realistic environment
In this study, we introduced security improvement to various cryptography methods to protect cryptography against fault attack.
In case study 1, we presented applying nonlinear fault discovery codes to defend elliptic curve point addition and doubling processes in contradiction to fault attacks for non-supersingular, supersingular, and Lopez-Dahab These ciphers provide practically perfect fault discovery capacity (beside from an exponentially small probability) at reasonable overhead. We presented error discovery structure by utilizing a fault discovery cipher. This error discovery structure has appeared to have over 99% error discovery coverage.
In case study 2, we presented applying nonlinear fault discovery codes to defend protect ECDSA operations contrary to error assaults.
In case study 3, we also presented applying the same methodology to defend Guillou-Quisquater authentication structure (GQ) contrary to error injection assaults.
In case study 4, we introduced a modification on supersingular isogeny cryptosystems operations by applying nonlinear error discovery ciphers to defend supersingular isogeny cryptosystems processes contrary to error assaults