**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

**Available format(s): **PDF | BibTeX Citation

**Note: **Thank you for pointing out some latex errors.

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

**Short URL: **ia.cr/2018/802

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