A New Approach to Post-Quantum Non-Malleability
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We provide the first 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡-𝑟𝑜𝑢𝑛𝑑 construction of post-quantum non-malleable commitments under the minimal assumption that 𝑝𝑜𝑠𝑡-𝑞𝑢𝑎𝑛𝑡𝑢𝑚 𝑜𝑛𝑒-𝑤𝑎𝑦 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠 exist. We achieve the standard notion of non-malleability with respect to commitments. Prior constructions required Ω(log^*λ) rounds under the same assumption. We achieve our results through a new technique for constant-round non-malleable commitments which is easier to use in the post-quantum setting. The technique also yields an almost elementary proof of security for constant-round non-malleable commitments in the classical setting, which may be of independent interest. As an application, when combined with existing work, our results yield the first constant-round post-quantum secure multiparty computation under the 𝑝𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙 hardness of quantum fully-homomorphic encryption and quantum learning with errors.
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