Quantum verifiable protocol for secure modulo zero-sum randomness

We propose a new cryptographic resource, secure modulo zero-sum randomness, as a resource to implement a task of secure modulo summation, and its quantum protocol. Secure modulo summation is the calculation of modulo summation Y1+⋯+Ym\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_1+\cdots + Y_m$$\end{document} when m players have their individual variables Y1,…,Ym\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_1,\ldots , Y_m$$\end{document} with keeping the secrecy of the individual variables. Secure modulo zero-sum randomness is a set of m variables X1,…,Xm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1, \ldots , X_m$$\end{document} held by m players that satisfy the zero sum condition X1+⋯+Xm=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1+\cdots + X_m=0$$\end{document} with a certain security condition. This paper explains the relation between these two concepts and proposes a quantum verifiable protocol for secure modulo summation. The advantage for quantum protocol is the verifiability based on self-testing, which does not need to trust measurement devices and can be realized by using a statistical concept, significance level, while any classical method needs to trust several components of the protocol. Then, we propose various cryptographic applications for secure modulo zero-sum randomness. We also compare our quantum verifiable protocol with the conventional method for secure modulo summation.