Signcryption schemes with threshold unsigncryption, and applications

The final publication is available at link.springer.comThe goal of a signcryption scheme is to achieve the same functionalities as encryption and signature together, but in a more efficient way than encrypting and signing separately. To increase security and reliability in some applications, the unsigncryption phase can be distributed among a group of users, through a (t, n)-threshold process. In this work we consider this task of threshold unsigncryption, which has received very few attention from the cryptographic literature up to now (maybe surprisingly, due to its potential applications). First we describe in detail the security requirements that a scheme for such a task should satisfy: existential unforgeability and indistinguishability, under insider chosen message/ciphertext attacks, in a multi-user setting. Then we show that generic constructions of signcryption schemes (by combining encryption and signature schemes) do not offer this level of security in the scenario of threshold unsigncryption. For this reason, we propose two new protocols for threshold unsigncryption, which we prove to be secure, one in the random oracle model and one in the standard model. The two proposed schemes enjoy an additional property that can be very useful. Namely, the unsigncryption protocol can be divided in two phases: a first one where the authenticity of the ciphertext is verified, maybe by a single party; and a second one where the ciphertext is decrypted by a subset of t receivers, without using the identity of the sender. As a consequence, the schemes can be used in applications requiring some level of anonymity, such as electronic auctions.Peer ReviewedPostprint (author's final draft

(Convertible) Undeniable Signatures without Random Oracles

We propose a convertible undeniable signature scheme without random oracles. Our construction is based on Waters\u27 and Kurosawa and Heng\u27s schemes that were proposed in Eurocrypt 2005. The security of our scheme is based on the CDH and the decision linear assumption. Comparing only the part of undeniable signatures, our scheme uses more standard assumptions than the existing undeniable signatures without random oracles due to Laguillamie and Vergnaud

(Hierarchical Identity-Based) Threshold Ring Signatures

We construct the first several efficient threshold ring signatures (TRS) without random oracles. Specializing to a threshold of one, they are the first several efficient ring signatures without random oracles after the only earlier instantiation of Chow, Liu, Wei, and Yuen. Further specializing to a ring of just one user, they are the short (ordinary) signatures without random oracles summarized in Wei and Yuen. We also construct the first hierarchical identity-based threshold ring signature without random oracles. The signature size is $O(n\lambda_s)$ bits, where $\lambda_s$ is the security parameter and $n$ is the number of users in the ring. Specializing to a threshold of one, it is the first hierarchical identity-based ring signature without random oracles. Further specializing to a ring of one user, it is the constant-size hierarchical identity-based signature (HIBS) without random oracles in Yuen-Wei - the signature size is $O(\lambda_s)$ bits which is independent of the number of levels in the hierarchy

Asynchronous distributed private-key generators for identity-based cryptography

An identity-based encryption (IBE) scheme can greatly reduce the complexity of sending encrypted messages over the Internet. However, an IBE scheme necessarily requires a private-key generator (PKG), which can create private keys for clients, and so can passively eavesdrop on all encrypted communications. Although a distributed PKG has been suggested as a way to mitigate this problem for Boneh and Franklin’s IBE scheme, the security of this distributed protocol has not been proven and the proposed solution does not work over the asynchronous Internet. Further, a distributed PKG has not been considered for any other IBE scheme. In this paper, we design distributed PKG setup and private key extraction protocols in an asynchronous communication model for three important IBE schemes; namely, Boneh and Franklin’s IBE, Sakai and Kasahara’s IBE, and Boneh and Boyen’s BB1-IBE. We give special attention to the applicability of our protocols to all possible types of bilinear pairings and prove their IND-ID-CCA security in the random oracle model. Finally, we also perform a comparative analysis of these protocols and present recommendations for their use.

Asynchronous Distributed Private-Key Generators for Identity-Based Cryptography

An identity-based encryption (IBE) scheme can greatly reduce the complexity of sending encrypted messages over the Internet. However, an IBE scheme necessarily requires a private-key generator (PKG), which can create private keys for clients, and so can passively eavesdrop on all encrypted communications. Although a distributed PKG has been suggested as a way to mitigate this problem for Boneh and Franklin\u27s IBE scheme, the security of this distributed protocol has not been proven and the proposed solution does not work over the asynchronous Internet. Further, a distributed PKG has not been considered for any other IBE scheme. In this paper, we design distributed PKG setup and private key extraction protocols in an asynchronous communication model for three important IBE schemes; namely, Boneh and Franklin\u27s IBE, Sakai and Kasahara\u27s IBE, and Boneh and Boyen\u27s BB1-IBE. We give special attention to the applicability of our protocols to all possible types of bilinear pairings and prove their IND-ID-CCA security in the random oracle model. Finally, we also perform a comparative analysis of these protocols and present recommendations for their use

Distributed Key Generation and Its Applications

Numerous cryptographic applications require a trusted authority to hold a secret. With a plethora of malicious attacks over the Internet, however, it is difficult to establish and maintain such an authority in online systems. Secret-sharing schemes attempt to solve this problem by distributing the required trust to hold and use the secret over multiple servers; however, they still require a trusted {\em dealer} to choose and share the secret, and have problems related to single points of failure and key escrow. A distributed key generation (DKG) scheme overcomes these hurdles by removing the requirement of a dealer in secret sharing. A (threshold) DKG scheme achieves this using a complete distribution of the trust among a number of servers such that any subset of servers of size greater than a given threshold can reveal or use the shared secret, while any smaller subset cannot. In this thesis, we make contributions to DKG in the computational security setting and describe three applications of it. We first define a constant-size commitment scheme for univariate polynomials over finite fields and use it to reduce the size of broadcasts required for DKG protocols in the synchronous communication model by a linear factor. Further, we observe that the existing (synchronous) DKG protocols do not provide a liveness guarantee over the Internet and design the first DKG protocol for use over the Internet. Observing the necessity of long-term stability, we then present proactive security and group modification protocols for our DKG system. We also demonstrate the practicality of our DKG protocol over the Internet by testing our implementation over PlanetLab. For the applications, we use our DKG protocol to define IND-ID-CCA secure distributed private-key generators (PKGs) for three important identity-based encryption (IBE) schemes: Boneh and Franklin's BF-IBE, Sakai and Kasahara's SK-IBE, and Boneh and Boyen's BB1-IBE. These IBE schemes cover all three important IBE frameworks: full-domain-hash IBEs, exponent-inversion IBEs and commutative-blinding IBEs respectively, and our distributed PKG constructions can easily be modified for other IBE schemes in these frameworks. As the second application, we use our distributed PKG for BF-IBE to define an onion routing circuit construction mechanism in the identity-based setting, which solves the scalability problem in single-pass onion routing circuit construction without hampering forward secrecy. As the final application, we use our DKG implementation to design a threshold signature architecture for quorum-based distributed hash tables and use it to define two robust communication protocols in these peer-to-peer systems