Cryptology ePrint Archive: Report 2018/802

Secure Modulo Zero-Sum Randomness as Cryptographic Resource

Masahito Hayashi and Takeshi Koshiba

Abstract: We propose a new cryptographic resource, which we call modulo zero-sum randomness, for several cryptographic tasks. The modulo zero-sum randomness $X_1, \ldots, X_m$ is distributed randomness among $m$ parties, where $X_1, \ldots, X_m$ are independent of each other but $\sum X_i =0$ holds. By using modulo zero-sum randomness, we show that multi-party secure computation for some additively homomorphic functions is efficiently realized without the majority honest nor secure communication channels (but public channel). We also construct secret sharing protocols without secure communication channels. Moreover, we consider a new cryptographic task multi-party anonymous authentication, which is realized by modulo zero-sum randomness. Furthermore, we discuss how to generate modulo zero-sum randomness from some information theoretic assumption. Finally, we give a quantum verification protocol of testing the property of modulo zero-sum randomness.

Category / Keywords: foundations / cryptographic resource, public channel, multi-party secure computation, secret sharing, authentication, quantum verification

Date: received 3 Aug 2018, last revised 10 Aug 2018

Contact author: tkoshiba at waseda jp

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Version: 20180906:174139 (All versions of this report)

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