Abu-Mahfouz, Adnan MIHancke, GP2010-01-222010-01-222009AbuMahouz, A.M.I. and Hancke, G.P. 2009. Efficient method for finding square roots for elliptic curves over OEF. 2009 International Conference on Foundations of Computer Science (FCS'09), Las Vegas, Nevada, USA, 13-16 July 2009, pp 87-911-60132-103-1http://hdl.handle.net/10204/39112009 International Conference on Foundations of Computer Science (FCS'09), Las Vegas, Nevada, USA, 13-16 July 2009Elliptic curve cryptosystems like others public key encryption schemes, require computing a square roots modulo a prime number. The arithmetic operations in elliptic curve schemes over Optimal Extension Fields (OEF) can be efficiently computed by using an irreducible binomial. This paper provides an overview of the OEF, Frobenius map and embedding points on an elliptic curve. The focus is on describing an efficient method to find a square root over Optimal Extension algorithm which is based on the Frobenius map, in order to simplify the problem of finding the square root over OEF.enSquare rootElliptic curveOptimal extension fieldFrobenius mapQuadratic residueConference PresentationAbu-Mahfouz, A. M., & Hancke, G. (2009). Efficient method for finding square roots for elliptic curves over OEF. http://hdl.handle.net/10204/3911Abu-Mahfouz, Adnan MI, and GP Hancke. "Efficient method for finding square roots for elliptic curves over OEF." (2009): http://hdl.handle.net/10204/3911Abu-Mahfouz AM, Hancke G, Efficient method for finding square roots for elliptic curves over OEF; 2009. http://hdl.handle.net/10204/3911 .TY - Conference Presentation AU - Abu-Mahfouz, Adnan MI AU - Hancke, GP AB - Elliptic curve cryptosystems like others public key encryption schemes, require computing a square roots modulo a prime number. The arithmetic operations in elliptic curve schemes over Optimal Extension Fields (OEF) can be efficiently computed by using an irreducible binomial. This paper provides an overview of the OEF, Frobenius map and embedding points on an elliptic curve. The focus is on describing an efficient method to find a square root over Optimal Extension algorithm which is based on the Frobenius map, in order to simplify the problem of finding the square root over OEF. DA - 2009 DB - ResearchSpace DP - CSIR KW - Square root KW - Elliptic curve KW - Optimal extension field KW - Frobenius map KW - Quadratic residue LK - https://researchspace.csir.co.za PY - 2009 SM - 1-60132-103-1 T1 - Efficient method for finding square roots for elliptic curves over OEF TI - Efficient method for finding square roots for elliptic curves over OEF UR - http://hdl.handle.net/10204/3911 ER -