# A Kilobit Hidden SNFS Discrete Logarithm Computation

@article{Fried2017AKH, title={A Kilobit Hidden SNFS Discrete Logarithm Computation}, author={Joshua Fried and Pierrick Gaudry and Nadia Heninger and Emmanuel Thom{\'e}}, journal={ArXiv}, year={2017}, volume={abs/1610.02874} }

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software.

## 47 Citations

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- Mathematics, Computer Science2021 IEEE 5th International Conference on Cryptography, Security and Privacy (CSP)
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This work proposes a new method to find the special number field sieve(SNFS) polynomial pair of a given prime, and recommends a simple ad-hoc detection of the trapdoor before doing the general numberField sieve (GNFS) to a prime $p$.

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This work addresses the question of degree 6 and aims at providing real-life timings for discrete logarithms in small degree extensions of finite fields of large characteristic, and shows how to improve many parts of the NFS-DL algorithm to reach this target.

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Two new records are reported: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 7 95-bit prime field, and it is shown that computing a discreteLogarithms is not much harder than a factorized number of the same size.

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The pre-computation phase for a 768-bit discrete logarithm problem, that allows for example to build a massive decryption tool of IPsec traffic protected by the Oakley group 1, was feasible in reasonable time using technologies available before the year 2000.

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- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
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This work combines the notions of threshold scheme and kleptographic attack to construct the first \(\ell \) out of n threshold klePTographic attack on discrete logarithm based digital signatures and prove its security in the standard and random oracle models.

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- Computer Science, MathematicsEUROCRYPT
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This work presents succinct two-party protocols for securely computing branching programs and \({\mathsf{NC}^1}\) circuits under the DDH assumption, providing the first alternative to fully homomorphic encryption.

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This work studies the best attacks against some of the most popular pairings and proposes new key sizes using an analysis which is more precise than the analysis in a recent article of Menezes, Sarkar and Singh.

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