Lightweight Asynchronous Verifiable Secret Sharing with Optimal Resilience

Abstract

We present new protocols for Asynchronous Verifiable Secret Sharing for Shamir (i.e., threshold t<n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t<n$$\\end{document}) sharing of secrets. Our protocols:Use only “lightweight” cryptographic primitives, such as hash functions;Can share secrets over rings such as Z/(pk)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}/(p^k)$$\\end{document} as well as finite fields Fq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {F}_q$$\\end{document};Provide optimal resilience, in the sense that they tolerate up to t<n/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t < n/3$$\\end{document} corruptions, where n is the total number of parties;Are complete, in the sense that they guarantee that if any honest party receives their share then all honest parties receive their shares;Employ batching techniques, whereby a dealer shares many secrets in parallel and achieves an amortized communication complexity that is linear in n, at least on the “happy path”, where no party provably misbehaves.