A modification of Shanks' baby-step giant-step algorithm

Abstract. I describe a modification to Shanks' baby-step giant-step algorithm for computing the order n of an element g of a group G, assuming n is finite. My method has the advantage of being able to compute n quickly, which Shanks' method fails to do when the order of G is infinite, unknown, or much larger than n. I describe the algorithm in detail. I also present the results of implementations of my algorithm, as well as those of a similar algorithm developed by Buchmann, Jacobson, and Teske, for calculating the order of various ideal classes of imaginary quadratic orders.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: David C. Terr
• Keywords: Algorithm, Baby-Step Giant-Step Algorithm, MOC 2000, Shanks