TITLE:
Asynchronous Secret Reconstruction and Its Application to the Threshold Cryptography
AUTHORS:
Lein Harn, Changlu Lin
KEYWORDS:
Shamir’s(t, n)Secret Sharing Scheme; Secret Reconstruction; Threshold Cryptography; Threshold Decryption; Asynchronous Networks
JOURNAL NAME:
International Journal of Communications, Network and System Sciences,
Vol.7 No.1,
January
16,
2014
ABSTRACT: In Shamir’s(t,n) threshold of the secret
sharing scheme, a secret is divided into n shares by a
dealer and is shared among n shareholders in
such a way that (a) the secret can be reconstructed when there are t or more than t shares; and (b)
the secret cannot be obtained when there are fewer than t shares. In the
secret reconstruction, participating users can be either legitimate
shareholders or attackers. Shamir’s scheme only considers the situation when
all participating users are legitimate shareholders. In this paper, we show
that when there are more than t users participating
and shares are released asynchronously in the secret reconstruction, an
attacker can always release his share last. In such a way, after knowing t valid shares of
legitimate shareholders, the attacker can obtain the secret and therefore, can
successfully impersonate to be a legitimate shareholder without being detected.
We propose a simple modification of Shamir’s scheme to fix this security
problem. Threshold cryptography is a research of group-oriented applications
based on the secret sharing scheme. We show that a similar security problem
also exists in threshold cryptographic applications. We propose a modified
scheme to fix this security problem as well.