Abstract
We present a new framework to design secure two-party computation protocols for exponentiation over integers and over Z Q where Q is a publicly-known prime. Using our framework, we realize efficient protocols in the semi-honest setting. Assuming the base is non-zero, and the exponent is at most Q/2 for the Z Q case, our protocols consist of at most 5 rounds (each party sending 5 messages) and the total communication consists of a small constant number (≤ 18) of encrypted/encoded elements in Z Q . Without these assumptions, our protocols are still more efficient than a protocol recently proposed by Damgård et al. in TCC 2006 (24 vs. > 114 rounds, ≈ 279ℓ + 12t for an error rate of 2− t vs. > 110 ℓlogℓ secure multiplications, where ℓ is the bit length of the shares).
Our protocols are constructed from different instantiations of our framework with different assumptions (homomorphic encryption or oblivious transfers) to achieve different advantages. Our key idea is to exploit the properties of both additive and multiplicative secret sharing. We also propose efficient transformation protocols between these sharings, which might be of independent interest.
A major part of the work was done while the second author was at New York University and the third author was at Harvard University. The third author is supported by US-Israel BSF grant 2006060 and NSF grant CNS-0831289.
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Yu, CH., Chow, S.S.M., Chung, KM., Liu, FH. (2011). Efficient Secure Two-Party Exponentiation. In: Kiayias, A. (eds) Topics in Cryptology – CT-RSA 2011. CT-RSA 2011. Lecture Notes in Computer Science, vol 6558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19074-2_2
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