R.J. Fateman. Polynomial multiplication, powers and asymptotic analysis: Some comments. SIAM J. Comput., 7(3):196--21, September 1974. Home/Search Document Not in Database Summary Related Articles Check |
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....before 1962, despite its comparatively simplicity and its usefulness, e.g. for mental arithmetic. Sedgewick [Sed90] also provides a description of the KOA in a compact notation, though slightly different from Knuth s. An investigation of the algorithm s computational complexity is given in [Fat74] where the KOA is referred to as Split. However, this reference contains an error in the derivation of the additive complexity, leading to a somewhat incorrect formula 1 . The KOA is based on the divide and conquer principle [Sed90] This principle is applied to suitable algorithms with ....
....2 m)T Phi : 5.16) Pi The overall complexities in the Theorems 9 and 10 are obtained by summation of the partial complexities. However, the right hand side of the additive complexity (5. 9) is an upper bound rather than an exact expression, because the recursive algorithm bears 2 Reference [Fat74] is here wrong by claiming that only 2 i Gamma 4 coefficients overlap. Multipliers over Composite Fields 47 redundancies which can be eliminated in a parallel realization. For instance, for the value m = 4, which is of great importance for the multiplier architectures to be developed, the ....
R.J. Fateman. Polynomial multiplication, powers and asymptotic analysis: Some comments. SIAM J. Comput., 7(3):196--21, September 1974.
Efficient Algorithms for Elliptic Curve Cryptosystems - Guajardo, Paar (1997) (11 citations) (Correct)
....In all cases, field multiplication is accomplished through table look up in the subfield GF (2 n ) Neither reference explores advanced convolution algorithms, such as the Karatsuba Ofman algorithm (KOA) as it is proposed here. The KOA has been studied for general polynomial multiplication in [3] and [7] An application of the KOA to polynomials over finite fields in the context of computer hardware is described in [19] None of the previous contributions provide a detailed complexity analysis of the algorithm as it is done in Sect. 5 of this work. Composite Galois fields are applied to a ....
R.J. Fateman. Polynomial multiplication, powers and asymptotic analysis: Some comments. SIAM J. Comput., 7(3):196--21, September 1974.
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