Abstract
This paper extends Joux-Naccache-Thomé’s e-th root algorithm to the static Diffie-Hellman problem (sdhp).
The new algorithm can be adapted to diverse finite fields by customizing it with an nfs-like core or an ffs-like core.
In both cases, after a number of non-adaptive sdhp oracle queries, the attacker builds-up the ability to solve new sdhp instances unknown before the query phase.
While sub-exponential, the algorithm is still significantly faster than all currently known dlp and sdhp resolution methods.
We explore the applicability of the technique to various cryptosystems.The attacks were implemented in \({\mathbb F}_{2^{1025}}\) and also in \({\mathbb F}_{p}\), for a 516-bit p.
Work partially supported by dga research grant 05.34.058.
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Joux, A., Lercier, R., Naccache, D., Thomé, E. (2009). Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_21
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DOI: https://doi.org/10.1007/978-3-642-10868-6_21
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