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- W2057250465 abstract "Let p and q be primes such that $p equiv 1 pmod q$. Let a be an integer such that ${a^{(p - 1)/q}} equiv 1 pmod p$. In 1972, H. C. Williams gave an algorithm which determines a solution of the congruence ${x^q} equiv a pmod p$ in $O({q^3}log p)$ steps, once an integer b has been found such that ${({b^q} - a)^{(p - 1)/q}} nequiv 0,1 pmod p$. A step is an arithmetic operation $pmod p$ or an arithmetic operation on q-bit integers. We present a refinement of this algorithm which determines a solution in $O({q^4}) + O({q^2}log p)$ steps, once b has been determined. Thus the new algorithm is better when q is small compared with p." @default.
- W2057250465 created "2016-06-24" @default.
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- W2057250465 date "1993-09-01" @default.
- W2057250465 modified "2023-09-25" @default.
- W2057250465 title "A refinement of H. C. Williams’ $q$th root algorithm" @default.
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- W2057250465 doi "https://doi.org/10.1090/s0025-5718-1993-1182249-0" @default.
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