Applications of Fast Truncated Multiplication in Embedded Cryptography

Truncated Multiplications compute Truncated Products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(n), with 1< α ≤ 2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications several cryptographic long integer arithmetic algorithms are improved, including integer reciprocals, divisions, Barrettand Montgomerymultiplications, 2n-digit modular multiplication on hardware for n-digit half products. E.g., Montgomery multiplication is performed in 2.6 Karatsuba multiplications time.