Abstract
We consider recent constructions of 1-out-of-N OT-extension from Kolesnikov and Kumaresan (CRYPTO 2013) and from Orrù et al. (CT-RSA 2017), based on binary error-correcting codes. We generalize their constructions such that q-ary codes can be used for any prime power q. This allows to reduce the number of base 1-out-of-2 OT’s that are needed to instantiate the construction for any value of N, at the cost of increasing the complexity of the remaining part of the protocol. We analyze these trade-offs in some concrete cases.
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Notes
- 1.
Of course, the elements of \(\{0,1\}\) could be identified with the elements of the field of two elements, \({\mathbb {F}}_2\). But for the sake of clarity, we will prefer to use \(\{0,1\}\) where we refer to bits and bitstrings and no algebraic properties are needed.
- 2.
The code is linear over \({\mathbb {F}}_q\), but not the alphabet \({\mathbb {F}}_q^s\).
- 3.
In Sect. 4, we show that this is still true if the protocol relies on a code over \({\mathbb {F}}_{p^r}\), and the consistency check is changed such that \(M'\in {\mathbb {F}}_p^{2s\times m}\).
- 4.
Shortening a code at positions \(i_1,\dots ,i_t\) means first taking the subcode consisting of all codewords with \(0's\) at all those positions and then erasing those coordinates.
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Acknowledgements
The authors wish to thank Claudio Orlandi for providing helpful suggestions during the early stages of this work, and Peter Scholl for his valuable comments.
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Cascudo, I., Christensen, R.B., Gundersen, J.S. (2018). Actively Secure OT-Extension from q-ary Linear Codes. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_18
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