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arXiv · 2309.00915

Manifesting Unobtainable Secrets: Threshold Elliptic Curve Key Generation using Nested Shamir Secret Sharing

J. L. Hall·Y. Hertzog·M. Loewy·M. P. Skerritt·D. Valladolid·G. Verma
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Abstract

We present a mechanism to manifest unobtainable secrets using a nested Shamir secret sharing scheme to create public/private key pairs for elliptic curves. A threshold secret sharing scheme can be used as a decentralised trust mechanism with applications in identity validation, message decryption, and agreement empowerment. Decentralising trust means that there is no single point vulnerability which could enable compromise of a system. Our primary interest is in twisted Edwards curves as used in EdDSA, and the related Diffie-Hellman key-exchange algorithms. The key generation is also decentralised, so can be used as a decentralised secret RNG suitable for use in other algorithms. The algorithms presented could be used to fill a ``[TBS]'' in the draft IETF specification ``Threshold modes in elliptic curves'' published in 2020 and updated in 2022.

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J. L. Hall, Y. Hertzog, M. Loewy, M. P. Skerritt, D. Valladolid, G. Verma. 2023-09-02. Manifesting Unobtainable Secrets: Threshold Elliptic Curve Key Generation using Nested Shamir Secret Sharing. https://arxiv.org/abs/2309.00915

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