Cryptology ePrint Archive: Report 2008/172

On Round Complexity of Unconditionally Secure VSS

Arpita Patra and Ashish Choudhary and Ashwinkumar B.V and C. Pandu Rangan

Abstract: In this work, we initiate the study of round complexity of {\it unconditionally secure weak secret sharing} (UWSS) and {\it unconditionally secure verifiable secret sharing} (UVSS) \footnote{In the literature, these problems are also called as statistical WSS and statistical VSS \cite{GennaroVSSSTOC01} respectively.} in the presence of an {\it all powerful} $t$-active adversary. Specifically, we show the following for UVSS: (a) 1-round UVSS is possible iff $t=1$ and $n>3$, (b) 2-round UVSS is possible if $n>3t$ and (c) 5-round {\it efficient} UVSS is possible if $n>2t$. For UWSS we show the following: (a) 1-round UWSS is possible iff $n>3t$ and (b) 3-round UWSS is possible if $n>2t$. Comparing our results with existing results for trade-off between fault tolerance and round complexity of perfect (zero error) VSS and WSS \cite{GennaroVSSSTOC01,FitziVSSTCC06,KatzVSSICALP2008}, we find that probabilistically relaxing the conditions of VSS/WSS helps to increase fault tolerance significantly.

Category / Keywords: Verifiable Secret Sharing, Error Probability, Information Theoretic Security

Date: received 15 Apr 2008, last revised 20 Jul 2008

Contact author: arpitapatra_10 at yahoo co in

Available formats: PDF | BibTeX Citation

Note: This paper is the combined version of our two papers titled "Probabilistic Verifiable Secret Sharing Tolerating Adaptive Adversary" and "Efficient Protocol for Generating IC Signature and its Application to Unconditional Verifiable Secret Sharing", which appeared earlier as ePrint Archive report no 2008/101 and 2008/172 respectively. The article 2008/172 was based on the improvement of the results of article 2008/101. However, there was a minor common bug in both the papers, which could be easily rectified. So instead of rectifying the bug separately in each paper, we corrected it and combined both the papers. We also changed the title of the combined paper as we found the new title to be more appropriate.

Version: 20080721:043528 (All versions of this report)

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