Abstract
We present two families of Boolean circuits of depth O(log n) and size n O(1) (P uniform), and of depth O(log n log log n) and size n O(1) (log-space uniform) for computing the modular inverse of an n-bit integer, where the modulus has only small prime factors. More precisely, this paper provides an NC 1 reduction of the problem mentioned above to integer division with remainder. In the case of P uniformity the circuits presented are asymptotically best possible.
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