Paper 2020/926

Secure Computation over Lattices and Elliptic Curves

Brett Hemenway Falk and Daniel Noble

Abstract

Traditional threshold cryptosystems have decentralized core cryptographic primitives like key generation, decryption and signatures. Most threshold cryptosystems, however, rely on special purpose protocols that cannot easily be integrated into more complex multiparty protocols. In this work, we design and implement decentralized versions of lattice-based and elliptic-curve-based public-key cryptoystems using generic secure multiparty computation (MPC) protocols. These are standard cryptosystems, so we introduce no additional work for encrypting devices and no new assumptions beyond those of the generic MPC framework. Both cryptosystems are also additively homomorphic, which allows for secure additions directly on ciphertexts. By using generic MPC techniques, our multiparty decryption protocols compute secret-shares of the plaintext, whereas most special-purpose cryptosystems either do not support decryption or must reveal the decryptions in the clear. Our method allows complex functions to be securely evaluated after decryption, revealing only the results of the functions and not the plaintexts themselves. To improve performance, we present a novel oblivious elliptic curve multiplication protocol and a new noise-masking technique which may be of independent interest. We implemented our protocols using the SCALE-MAMBA secure multiparty computation platform, which provides security against malicious adversaries and supports arbitrary numbers of participants.