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The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most n log 2 ⁡ 3 ≈ n 1.58 {\displaystyle n^{\log _{2}3}\approx n^{1.58}} single-digit multiplications. It is therefore asymptotically faster than the traditional algorithm, which performs n 2 {\displaystyle n^{2}} single-digit products. The Karatsuba algorithm was the first multiplication algorithm asymptotically faster than the quadratic "grade school" algorithm. The Toom–Cook algorithm (1963) is a faster generalization of Karatsuba's method, and the Schönhage–Strassen algorithm (1971) is even faster, for sufficiently large n.