Cryptosystems based on (Elligator-style) Edwards elliptic curves

• Grant number: 14/09200-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2014
• End date: June 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
• Principal Investigator: Paulo Sérgio Licciardi Messeder Barreto
• Grantee: Gustavo Henrique Muriel Zanon
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

We propose to investigate the aspects of computational performance as well as data and program storage requirements of cryptosystems based on Edwards elliptic curves, specifically those that can be obtained through the Elligator methodology, so as to avoid accidental or intentional hidden vulnerabilities. This research will cover not only the lower security levels (i.e. from legacy 2**80 to the current business standard 2**128), but also, and mainly, the higher security levels (2**192 to 2**256) as needed for the deployment of a wide-scope certification hierarchy like ICP-Brasil.