Patent ID: 7363336

Claim:
A computer-readable medium having computer-executable instructions for securing data that, when executed by a computer, performs acts comprising: obtaining two input polynomials each with degree 5, wherein a first polynomial is nominally described as a ( X )= a 0 a 1 X+a 2 X 2 +a 3 X 3 +a 4 X 4 +a 5 X 5 and a second polynomial is nominally described as b ( X )= b 0 +b 1 X+b 2 X 2 +b 3 X 3 +b 4 X 4 +b 5 X 5 and terms a 5 and b 5 are non-zero values; computing a product polynomial of the input polynomials, wherein the total number of coefficient multiplication operations is fewer than or equal to seventeen, wherein during the computing, calculating: ( a 0 +a 1 +a 2 +a 3 +a 4 +a 5 )( b 0 +b 1 +b 2 +b 3 +b 4 +b 5 ) C+ ( a 1 +a 2 +a 4 +a 5 )( b 1 +b 2 +b 4 +b 5 )( −C+X 6 )+( a 0 +a 1 +a 3 +a 4 )( b 0 +b 1 +b 3 +b 4 )( −C+X 4 )+( a 0 −a 2 −a 3 +a 5 ) ( b 0 −b 2 −b 3 +b 5 )( C−X 7 +X 6 −X 5 +X 4 −X 3 )+( a 0 −a 2 −a 5 )( b 0 −b 2 −b 5 )( C−X 5 +X 4 −X 3 )+( a 0 +a 3 −a 5 )( b 0 +b 3 −b 5 )( C−X 7 +X 6 −X 5 )+( a 0 +a 1 +a 2 )( b 0 +b 1 +b 2 ) ( C−X 7 +X 6 −2 X 5 +2 X 4 −2 X 3 +X 2 )+( a 3 +a 4 +a 5 )( b 3 +b 4 +b 5 )( C+X 8 −2 X 7 +2 X 6 −2 X 5 +X 4 −X 3 )+( a 2 +a 3 )( b 2 +b 3 )(−2 C+X 7 −X 6 +2 X 5 −X 4 +X 3 )+( a 1 −a 4 )( b 1 −b 4 ) ( −C+X 4 X 5 X 6 )+( a 1 +a 2 )( b 1 +b 2 )( −C+X 7 −2 X 6 −2 X 5 −2 X 4 +3 X 3 −X 2 )+( a 3 +a 4 )( b 3 +b 4 )( −C−X 8 +3 X 7 −2 X 6+ 2 X 5 −2 X 4 +X 3 )+( a 0 +a 1 )( b 0 +b 1 ) (− C+X 7 −X 6 +2 X 5 −3 X 4 +2 X 3 −X 2 +X )+( a 4 +a 5 )( b 4 +b 5 )( −C+X 9 −X 8 +2 X 7 −3 X 6 +2 X 5 −X 4 +X 3 )+ a 0 b 0 (−3 C +2 X 7 −2 X 6 +3 X 5 −2 X 4 +2 X 3 −X +1)+ a 1 b 1 (3 C−X 7 −X 5 +X 4 −3 X 3 +2 X 2 −X )+ a 4 b 4 (3 C−X 9 +2 X 8 −3 X 7 +X 6 −X 5 −X 3 )+ a 5 b 5 (−3 C+X 10 −X 9 +2 X 7 −2 X 6 +3 X 5 −2 X 4 +2 X 3 ) to compute the product polynomial; reporting results of the computing, whereby the computed results facilitate data security.