The CREW PRAM Complexity of Modular Inversion

One of the long-standing open questions in the theory of parallel computation is the parallel complexity of the integer gcd and related problems, such as modular inversion. We present a lower bound (logn) for the parallel time on an exclusive-write parallel random access machine (CREW PRAM) computingthe inverse modulocertain n-bit integers, includingall such primes. For in nitelymany moduli,our lower boundmatchesasymptoticallythe known upper bound. We obtain a similar lower bound for computing a speci ed bit in a large power of an integer. Our main tools are certain estimates for exponential sums in nite elds.

• Type: Conference
• Year: 1998
• Where: LATIN
• Authors: Joachim von zur Gathen, Igor Shparlinski
• Keywords: Information Management, LATIN 1998, Lower Bound, Parallel Random Access Machine, Similar Lower Bound