Patent Document ID: 7765252
Application ID: 10805564
Patent Flag: 1

Claim One:
1. A computer storage medium storing computer-executable instructions that, when executed by a computer, configure the computer as a Karatsuba-variant calculator to electronically secure digital data by performing acts comprising: receiving as input, a pair of polynomials: 
 a ( X )= a 0 +a 1 X+a 2 X 2 +a 3 X 3 +a 4 X 4 and 
 b ( X )= b 0 +b 1 X+b 2 X 2 +b 3 X 3 +b 4 X 4 computing a product polynomial of the pair of polynomials by calculating ( a 0 + a 1 + a 2 + a 3 + a 4 ) ⁢ ( b 0 + b 1 + b 2 + b 3 + b 4 ) ⁢ ( X 5 - X 4 + X 3 ) + ( a 0 - a 2 - a 3 - a 4 ) ⁢ ( b 0 - b 2 - b 3 - b 4 ) ⁢ ( X 6 - 2 ⁢ X 5 + 2 ⁢ X 4 - X 3 ) + ( a 0 + a 1 + a 2 - a 4 ) ⁢ ( b 0 + b 1 + b 2 - b 4 ) ⁢ ( - X 5 + 2 ⁢ X 4 - 2 ⁢ X 3 + X 2 ) + ( a 0 + a 1 - a 3 - a 4 ) ⁢ ( b 0 + b 1 - b 3 - b 4 ) ⁢ ( X 5 - 2 ⁢ X 4 + X 3 ) + ( a 0 - a 2 - a 3 ) ⁢ ( b 0 - b 2 - b 3 ) ⁢ ( - X 6 + 2 ⁢ X 5 - X 4 ) + ( a 1 + a 2 - a 4 ) ⁢ ( b 1 + b 2 - b 4 ) ⁢ ( - X 4 + 2 ⁢ X 3 - X 2 ) + ( a 3 + a 4 ) ⁢ ( b 3 + b 4 ) ⁢ ( X 7 - X 6 + X 4 - X 3 ) + ( a 0 + a 1 ) ⁢ ( b 0 + b 1 ) ⁢ ( - X 5 + X 4 - X 2 + X ) + ( a 0 - a 4 ) ⁢ ( b 0 - b 4 ) ⁢ ( - X 6 + 3 ⁢ X 5 - 4 ⁢ X 4 + 3 ⁢ X 3 - X 2 ) + a 4 ⁢ b 4 ⁡ ( X 8 - X 7 + X 6 - 2 ⁢ X 5 + 3 ⁢ X 4 - 3 ⁢ X 3 + X 2 ) + a 3 ⁢ b 3 ⁡ ( - X 7 + 2 ⁢ X 6 - 2 ⁢ X 5 + X 4 ) + a 1 ⁢ b 1 ⁡ ( X 4 - 2 ⁢ X 3 + 2 ⁢ X 2 - X ) + a 0 ⁢ b 0 ⁡ ( X 6 - 3 ⁢ X 5 + 3 ⁢ X 4 - 2 ⁢ X 3 + X 2 - X + 1 ) ; outputting the product of the pair of polynomials; and electronically securing digital data by using the product of the pair of polynomials.