Fast Truncated Multiplication for Cryptographic Applications

The Truncated Multiplication computes a truncated product, a contiguous subsequence of the digits of the product of 2 integers. A few truncated polynomial multiplication algorithms are presented and adapted to integers. They are based on the most often used n-digit full multiplication algorithms of time complexity O(n), with 1< α ≤ 2, but a constant times faster. For example, the least significant half products with Karatsuba multiplication need only 80% of the full multiplication time. The faster the multiplication, the less relative time saving can be achieved.