Tight upper bounds for polynomial multiplication

Efficient arithmetic over finite fields has high relevance both in hardware and software implementations. One of the most expensive operation over finite field is the multiplication. To our knowledge, the best known explicit upper bounds for the polynomial multiplication were obtained using the multiplication technique presented in [3]. In this paper, we improve such explicit upper bounds and show how this research allows us to reduce the number of bit operations needed to multiply m-bit polynomials. Key–Words: Polynomial multiplication, Karatsuba algorithm, optimizations, AND/XOR gates

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