Multiplierless Design of Very Large Constant Multiplications in Cryptography

This brief addresses the problem of implementing very large constant multiplications by a single variable under the shift-adds architecture using a minimum number of adders/subtractors. Due to the intrinsic complexity of the problem, we introduce an approximate algorithm, called TÕLL, which partitions the very large constants into smaller ones. To reduce the number of operations, TÕLL incorporates graph-based and common subexpression elimination methods proposed for the shift-adds design of constant multiplications. It can also consider the delay of a multiplierless design defined in terms of the maximum number of operations in series, i.e., the number of adder-steps, while reducing the number of operations. High-level experimental results show that the adder-steps of a shift-adds design can be reduced significantly with a little overhead in the number of operations. Gate-level experimental results indicate that while the shift-adds design can lead to a 36.6% reduction in gate-level area with respect to a design using a multiplier, the delay-aware optimization can yield a 48.3% reduction in minimum achievable delay of the shift-adds design when compared to the area-aware optimization.