Efficient and Unconditionally Secure Digital Signatures and a Security Analysis of a Multireceiver Authentication Code

Abstract

Digital signatures whose security does not rely on any unproven computational assumption have recently received considerable attention. While these unconditionally secure digital signatures provide a foundation for long term integrity and non-repudiation of data, currently known schemes generally require a far greater amount of memory space for the storage of users' secret information than a traditional digital signature. The focus of this paper is on methods for reducing memory requirements of unconditionally secure digital signatures. A major contribution of this paper is to propose two novel unconditionally secure digital signature schemes that have significantly shortened secret information for users. As a specific example, with a typical parameter setting the required memory size for a user is reduced to approximately 1 10 of that in previously known schemes. Another contribution of the paper is to demonstrate an attack on a multireceiver authentication code proposed by Safavi-Naini and Wang, and present a method to fix the problem of the code.

Unconditionally secure signature schemes revisited

“…The models of Hanaoka et al [5,6] and Safavi-Naini et al [10] are based on security notions from message authentication codes (MACs). Hanaoka et al treat only a limited attack scenario (which is covered by our model), including impersonation, substitution, and transfer with a trap, and do not include a verification oracle.…”

“…That is, it is important to distinguish between signatures that are created using a user's signing algorithm and signatures that may satisfy one or more user verification algorithms. Current research [5,6,10,12,7] has proposed various models for unconditionally secure signature schemes, but these models do not fully treat the implications of having multiple verification algorithms or analyze the need for (and trust questions associated with) having a dispute resolution mechanism. We address both of these issues in this paper.…”

“…Unsurprisingly, the first security models for unconditionally secure signature schemes, including Johansson [9] and Hanaoka et al [5,6], drew upon the standard MAC security models. Shikata et al [12] introduced a model using notions from public-key cryptography, which was also adopted in the work by Hara et al [7] on blind signatures.…”

“…Safavi-Naini et al [10] presented a MAC-based model meant to encompass the notions developed by Shikata et al In this work, we present a new security model. Our model is more general than the MAC-based models of Hanaoka et al [5,6] and Safavi-Naini et al [10] and covers the attacks described in these works. Like that of Shikata et al [12], our work is based on security notions from traditional public-key signature systems.…”

Unconditionally Secure Anonymous Encryption and Group Authentication

“…no anonymity. Though there are some unconditionally secure digital signature schemes [19,20,26] that do exist, these schemes yet too, do not provide anonymity. However, in computationally secure settings, anonymity can be achieved by using group signatures [11,8].…”