Avoiding Full Extension Field Arithmetic in Pairing Computations

Abstract. The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operat...

• Type: Conference
• Year: 2010
• Where: AFRICACRYPT
• Authors: Craig Costello, Colin Boyd, Juan Manuel González Nieto, Kenneth Koon-Ho Wong
• Keywords: AFRICACRYPT 2010, Costly Operations, Cryptology, Extension field Fpk, Extension field Operations