The predecessor to the Fürer algorithm, the Schönhage–Strassen algorithm, used fast Fourier transforms to compute integer products in time (in big O notation) and its authors, Arnold Schönhage and Volker Strassen, also conjectured a lower bound for the problem of . Here, denotes the total number of bits in the two input numbers. Fürer's algorithm reduces the gap between these two bounds: it can be used to multiply binary integers of length in time (or by a circuit with that many logic gates), where log*n represents the iterated logarithm operation. However, the difference between the and factors in the time bounds of the Schönhage–Strassen algorithm and the Fürer algorithm for realistic values of is very small.
In 2008, Anindya De, Chandan Saha, Piyush Kurur and Ramprasad Saptharishi gave a similar algorithm that relies on modular arithmetic instead of complex arithmetic to achieve the same running time.