On the Cryptographic Value of the q th Root Problem

Beaver, Cheryl; Gemmell, Peter; Johnston, Anna M.; Neumann, William Douglas

doi:10.1007/978-3-540-47942-0_11

Cited by 2 publications

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“…Cipolla [3] used the fact that q n+1 |(P q − 1) along with properties of the norm of elements in F P q to design a square root algorithm (q = 2) over F P . This algorithm is easily extended to compute qth roots for any prime q [1] and avoids the generally required discrete logarithm computation for n > 1 [2,4].…”

Section: Introductionmentioning

confidence: 99%

Trace formulae for irreducible polynomials over FP with minimal order roots in FPq

Johnston

2008

Finite Fields and Their Applications

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The extension field F P q where q is a prime divisor of (P −1), has a unique structure. This paper describes this unique structure and uses it to derive formulas relating the trace values for elements in F P q . These formulas can be refined for certain elements to produce a formula for the trace. BackgroundWhen q is a prime divisor of (P − 1), the extension field F P q has a unique structure. This structure is based on the factorization of (P q − 1) with respect to (P − 1) and q.Let q be a prime withwhere n 1, and gcd(q, s) = 1. Cipolla [3] used the fact that q n+1 |(P q − 1) along with properties of the norm of elements in F P q to design a square root algorithm (q = 2) over F P . This algorithm is easily extended to compute qth roots for any prime q [1] and avoids the generally required discrete logarithm computation for n > 1 [2,4].

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Section: Introductionmentioning

confidence: 99%