Type of Document Thesis Author Maneva-Jakimoska, Karolina Author's Email Address email@example.com URN etd-04092006-135341 Title Anonymous T-out-of-N Threshold Signature Schemes Degree Master of Science Department Computer Science, Department of Advisory Committee
Advisor Name Title Mike Burmester Committee Chair Alec Yasinsac Committee Member Breno DeMedeiros Committee Member Keywords
- Covering Design
- Threshold Signature Schemes
- Vandermonde Matrix
Date of Defense 2006-04-03 Availability unrestricted AbstractIn many multi-user cryptographic applications (e.g., electronic voting, digital lotteries, e-cash application, anonymous access to some resources,
etc.), anonymity pops up as one of the main security objectives.
Protecting private information about the involved users is not only desirable but crucial for existence and proper working of these applications.
Group signatures were the first signatures to provide anonymity of the signer(s): the members of the group can anonymously sign messages on behalf of the group using specially designed keys.
The keys used by the individual members of the group are generated and distributed by a trusted group manager.
Hence, group signatures are suitable for cooperative groups that have some preexisting structure.
They are not suitable for groups that can be formed in an ad-hoc manner. To solve this problem, Rivest, Shamir and Tauman
(ASIACRYPT 2001) introduced the notion of ring signature schemes.
Unlike group signatures, ring signatures have no group managers.
Any user can select a set (ring) of possible signers that includes himself, and using his private key and the public key of the other member of the ring, he can sign on behalf of the ring.
Bresson, Stern and Szydlo (CRYPTO 2002) extend the notion to a threshold setting where some minimum number t of members of the group has to cooperate in order to sign a message.
The complexity of the threshold ring signature scheme proposed by Bresson et al is prohibitively large even for relatively small sets of signers.
Our contribution: We propose two new anonymous signature schemes. The first one is a threshold ring signature scheme that is constructed using covering designs. This scheme is efficient even for large groups of signers. The cost we pay is that anonymity is not perfect although it remains unconditional.
The other one is a threshold scheme that is based on Vandermonde matrices. The second scheme is not always as efficient as the first one.
However, it provides unconditional and perfect anonymity.
In a threshold ring signature scheme, any subset of members whose size is not below the threshold t can generate a signature. However, in some situations, we want to be able to specify which subsets can sign.
We go beyond threshold ring signatures and propose a scheme where the possible subsets of actual signers are defined by a general access structure.
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