Fast Exponentiation Using Split Exponents

Abstract—We propose a new method to speed up discrete logarithm (DL)-based cryptosystems by considering a new variant of the DL problem, where the exponents are formed as e1 + αe2 for some fixed α and two integers e1, e2 with a low weight representation. We call this class of exponents split exponents, and we show that with certain choice of parameters the DL problem on split exponents is essentially as secure as the standard DL problem, while the exponentiation operation using exponents of this class is significantly faster than best exponentiation algorithms given for standard exponents. For example, the speed of scalar multiplication on the standard Koblitz curve K163 is

• Type: Journal
• Year: 2011
• Where: TIT
• Authors: Jung Hee Cheon, Stanislaw Jarecki, Taekyoung Kwon, Mun-Kyu Lee
• Keywords: DL Problem, Education, Split Exponents, Standard Dl Problem, TIT 2011