On efficient techniques for difficult operations in one and two-digit DBNS index calculus

The Double Base Number System (DBNS), using orthogonal bases of 2 and 3, has similar properties to the logarithmic number system (LNS) if an index calculus is used. The DBNS provides more degrees of freedom than the LNS by virtue of both the orthogonal bases and the ability to use multiple digits. As with the LNS, multiplication and division are easy but addition and subtraction are difficult. This paper introduces a technique that uses a map to a DBNS "index sequence domain", removing the need for the relatively large look-up table solution of the LNS.