Calculating optimal addition chains

DOI10.1007/s00607-010-0118-8zbMath1241.11139OpenAlexW2147037654WikidataQ55953253 ScholiaQ55953253MaRDI QIDQ644848

Neill Michael Clift

Publication date: 7 November 2011

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-010-0118-8

zbMATH Keywords

optimizationsequencesexponentiationaddition chainsScholz-Brauer conjecture

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Directed graphs (digraphs), tournaments (05C20) Calculation of integer sequences (11Y55)

Related Items (5)

Internal structure of addition chains: well-ordering ⋮ Addition chains, vector chains, and efficient computation ⋮ IMPROVEMENT OF THE LOWER BOUND FOR THE COMPLEXITY OF EXPONENTIATION ⋮ Low-cost addition-subtraction sequences for the final exponentiation in pairings ⋮ Koblitz curves over quadratic fields

Uses Software

• OEIS

Cites Work

• Addition chains and solutions of \(\ell(2n)=\ell(n)\) and \(\ell(2^n-1)= n+\ell(n)-1\)
• Integers with a small number of minimal addition chains
• The Scholz-Brauer problem on addition chains
• A public key cryptosystem and a signature scheme based on discrete logarithms
• A Survey of Fast Exponentiation Methods
• Efficient Generation of Minimal Length Addition Chains
• Some Properties of Nonstar Steps in Addition Chains and New Cases Where the Scholz Conjecture Is True
• A Lower Bound for the Scholz-Brauer Problem
• On addition chains
• A Note on the Scholz-Brauer Problem in Addition Chains
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