FFT puzzle - convolution without an inverse FFT

This is a puzzle for those who know Fourier transform math.  Suppose you want to do a circular convolution of two complex-valued sequences A and B, each of length n.   It's well known that you can do it by:

  1. Use a forward FFT to transform A and B into sequences a and b respectively.
  2. Do elementwise multiplication of a and b.to generate a sequence c.
  3. Use a backward (inverse) FFT on c to get the product C=A*B

Now suppose you are stranded on a desert isle with a computer that does only forward FFTs.  Can you still do convolutions using a process similar to the above, without using a backward FFT?  How?

- Arch

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