Bilinear Diffie-Hellman Problem Research Articles

Efficient signcryption between TPKC and IDPKC and its multi-receiver construction

The primitive signcryption provides authenticity and privacy simultaneously. In this paper, we present efficient signcryption schemes between the traditional public key cryptosystem (TPKC) and the identity based cryptosystem (IDPKC). In contrast, all the existing signcryption schemes available in the literature, to our knowledge, are limited to within one type of cryptosystem. We also discuss them in the multi-receiver setting. Formal security proofs are provided to guarantee the security for our schemes, in the random oracle model, under the hardness of the bilinear Diffie-Hellman problem.

K out of n Oblivious Transfer Protocols from Bilinear Pairings

T wo non-interactive three parties k out of n oblivious transfer protocols from bilinear pairings are proposed i n this paper. In these protocols , a sender can obliviously transfer n messages to a receiver without communication with him/her. The public keys that a sender used to encrypt his/her messages are made by a third party. The receiver can extract k out of n messages at his/her choices by using the corresponding secret keys. The choices of the receiver are unconditionally secure. The sender's secrecy is guaranteed if the receiver is semi-honest in the standard model since the decision bilinear Diffie-Hellman problem (DBDH) is hard and the sender's secrecy is achieved when the receiver is a malicious party in the random oracle model since the bilinear Diffie-Hellman problem assumption (BDHA) holds. When a sender is a cheating party, the receiver will detect him/her and halt the protocol. A precise proof of the security of the protocols is presented.

Perfect forward secure identity-based authenticated key agreement protocol in the escrow mode

The majority of existing escrowable identity-based key agreement protocols only provide partial forward secrecy. Such protocols are, arguably, not suitable for many real-word applications, as the latter tends to require a stronger sense of forward secrecy—perfect forward secrecy. In this paper, we propose an efficient perfect forward-secure identity-based key agreement protocol in the escrow mode. We prove the security of our protocol in the random oracle model, assuming the intractability of the Gap Bilinear Diffie-Hellman (GBDH) problem.

An ID-based group-oriented decryption scheme secure against adaptive chosen-ciphertext attacks

ID-based decryption allows a sender to encrypt a message to an identity without access to a public key certificate. This paper proposes an ID-based group-oriented decryption scheme, secure against adaptive chosen-ciphertext attacks, which allows the sender to determine an access structure and generate a valid ciphertext on the chosen message. The correctness of decryption shares can be checked to detect when dishonest users in the access structure provide fake decryption shares. As a result, the message can be cooperatively recovered by users in the determined access structure. The formal proof of security of our scheme is based on the bilinear Diffie–Hellman problem in the random oracle model. Our proposed scheme is more efficient and provides higher security confidence than those in Li et al.’s certificate-based group-oriented decryption scheme.

The Diffie–Hellman problem and generalization of Verheul’s theorem

Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear Diffie–Hellman problem. In contrast to the discrete log (or Diffie–Hellman) problem in a finite field, the difficulty of this problem has not yet been much studied. In 2001, Verheul (Advances in Cryptology—EUROCRYPT 2001, LNCS 2045, pp. 195–210, 2001) proved that on a certain class of curves, the discrete log and Diffie–Hellman problems are unlikely to be provably equivalent to the same problems in a corresponding finite field unless both Diffie–Hellman problems are easy. In this paper we generalize Verheul’s theorem and discuss the implications on the security of pairing based systems.

Designated verifier proxy signature scheme without random oracles

In a designated verifier proxy signature scheme, one can delegate his or her signing capability to another user in such a way that the latter can sign messages on behalf of the former, but the validity of the resulting signatures can only be verified by the designated verifier. Several designated verifier proxy signature schemes have been proposed so far. However, most of the schemes were proven secure in the random oracle model, which has received a lot of criticism since the security proofs in the random oracle model are not sound with respect to the standard model. In this paper, we propose a new construction of designated verifier proxy signature whose security can be proven without using the random oracle model. Our scheme is inspired by Waters’ Identity-based encryption. The unforgeability of our scheme is based on the hardness of Gap Bilinear Diffie–Hellman problem. As far as we know, this is the first designated verifier proxy signature secure in the standard model.

Identity-based encryption with wildcards in the standard model

In this article, based on Chatterjee-Sarkar' hierarchical identity-based encryption (HIBE), a novel identity-based encryption with wildcards (WIBE) scheme is proposed and is proven secure in the standard model (without random oracle). The proposed scheme is proven to be secure assuming that the decisional Bilinear Diffie-Hellman (DBDH) problem is hard. Compared with the Wa-WIBE scheme that is secure in the standard model, our scheme has shorter common parameters and ciphertext length.

NEW EXTENSIONS OF PAIRING-BASED SIGNATURES INTO UNIVERSAL (MULTI) DESIGNATED VERIFIER SIGNATURES

The concept of universal designated verifier signatures was introduced by Steinfeld, Bull, Wang and Pieprzyk at Asiacrypt 2003. These signatures can be used as standard publicly verifiable digital signatures but have an additional functionality which allows any holder of a signature to designate the signature to any desired verifier. This designated verifier can check that the message was indeed signed, but is unable to convince anyone else of this fact. We propose new efficient constructions for pairing-based short signatures. Our first scheme is based on Boneh-Boyen signatures and its security can be analyzed in the standard security model. We prove its resistance to forgery assuming the hardness of the so-called strong Diffie-Hellman problem, under the knowledge-of-exponent assumption. The second scheme is compatible with the Boneh-Lynn-Shacham signatures and is proven unforgeable, in the random oracle model, under the assumption that the computational bilinear Diffie-Hellman problem is untractable. Both schemes are designed for devices with constrained computation capabilities since the signing and the designation procedure are pairing-free. Finally, we present extensions of these schemes in the multi-user setting proposed by Desmedt in 2003.

Secure proxy re-encryption from CBE to IBE

In this paper, an efficient hybrid proxy re-encryption scheme that allows the transformation of the ciphertexts in a traditional public key cryptosystem into the ciphertexts in an identity-based system is proposed. The scheme is non-interactive, unidirectional and collude “safe”. Furthermore, it is compatible with current IBE (identity-based encryption) deployments. The scheme has chosen ciphertext security in the random oracle model assuming the hardness of the Decisional Bilinear Diffie-Hellman problem.

Identity-Based Encryptions with Tight Security Reductions to the BDH Problem

We present IND-ID-CPA secure identity-based encryption (IBE) schemes with tight reductions to the bilinear Diffie-Hellman (BDH) problem. Since the methods for obtaining IND-ID-CCA secure schemes from IND-ID-CPA secure schemes with tight reductions are already known, we can consequently obtain IND-ID-CCA secure schemes with tight reductions to the BDH problem. Our constructions are based on IBE schemes with tight reductions to the list bilinear Diffie-Hellman (LBDH) problem, and the schemes are converted to those with tight reductions to the BDH problem. Interestingly, it can be shown that there exists a black box construction, in which the former IBE schemes are given as black boxes. Our constructions are very simple and reasonably efficient.

General Group Oriented ID-Based Cryptosystems with Chosen Plaintext Security

A scheme for general group oriented ID-based cryptosystems is proposed. This scheme allows an authorized subset in the general access structure to cooperatively decrypt the ciphertext of a message. It is constructed using bi-linear pairings. Its security is based on the intractability of the computational bilinear Diffie-Hellman problem. The scheme possesses chosen-plaintext security in the random oracle model.

Identity based signcryption scheme without random oracles

Many identity based signcryption schemes have been proposed so far. However, all the schemes were proven secure in the random oracle model which has received a lot of criticism that the proofs in the random oracle model are not proofs. In this paper, motivated by Waters' identity based encryption scheme, we propose the first identity based signcryption scheme without random oracles. We prove that the proposed scheme is secure in the standard model. Specifically, we prove its semantic security under the hardness of Decisional Bilinear Diffie–Hellman problem and its unforgeability under the Computational Diffie–Hellman assumption.

Certificateless universal designated verifier signature schemes

Universal designated verifier signature schemes allows a signature holder to designate the signature to a desire designated verifier, in such a way that only designated verifier can verify this signature, but is unable to convince anyone else of this fact. The previous constructions of universal designated verifier signature rely on the underlying public key infrastructure, that needs both signers and verifiers to verify the authenticity of the public keys, and hence, the certificates are required. This article presents the first model and construction of the certificateless universal designated verifier signature scheme, in which the certificates are not needed. The proposed scheme satisfies all the requirements of the universal designated verifier signature in the certificateless system. Security proofs are provided for the scheme based on the random oracle model, assuming that the Bilinear diffie-hellman (BDH) problem is hard to solve.

A novel ID-based designated verifier signature scheme

In a designated verifier signature scheme, only the designated verifier can verify the validity of a signature. This paper studies an Identity-based Strong Designated Verifier Signature (IBSDVS) scheme based on bilinear pairings by combining ID-based cryptosystem with the designated verifier signature scheme. We analyze the security of the scheme and the result shows that the security of our proposed scheme is closely related to the Bilinear Diffie–Hellman problem and the scheme is against delegatability attack.

Certificateless threshold cryptosystem secure against chosen-ciphertext attack

This paper proposes the first certificateless threshold decryption scheme which avoids both the single point of failure in the distributed networks and the inherent key escrow problem in identity-based cryptosystem. The scheme is secure against threshold chosen-ciphertext attack. It tolerates the Type I adversary that can replace public key and the Type II adversary that has access to the system’s master key. The formal proof of security is presented in the random oracle model, assuming some underlying problems closely related to the Bilinear Diffie–Hellman Problem are computationally hard.

Secure mediated certificateless signature scheme

Ju et al. proposed a certificateless signature scheme with instantaneous revocation by introducing security mediator (SEM) mechanism. This article presents a detailed cryptoanalysis of this scheme and shows that, in their proposed scheme, once a valid signature has been produced, the signer can recover his private key information and the instantaneous revocation property will be damaged. Furthermore, an improved mediated signature scheme, which can eliminate these disadvantages, is proposed, and security proof of the improved scheme under elliptic curve factorization problem (ECFP) assumption and bilinear computational diffie-hellman problem (BCDH) assumption is also proposed.

ID-based threshold decryption secure against adaptive chosen-ciphertext attack

This paper proposes an identity-based threshold decryption scheme IB-ThDec and reduces its security to the Bilinear Diffie–Hellman problem. Compared with previous work, this conceals two pairing computations in the ciphertext validity verification procedure. The formal proof of security of this scheme is provided in the random oracle model. Additionally, we show that IB-ThDec can be applied to the threshold key escrow and the mediated cryptosystems.

Provably secure non-interactive key distribution based on pairings

We define a security notion for non-interactive key distribution protocols. We identify an apparently hard computational problem related to pairings, the Bilinear Diffie-Hellman problem (BDH). Afte...

Adaptive Chosen Ciphertext Secure Threshold Key Escrow Scheme from Pairing

This paper proposes a threshold key escrow scheme from pairing. It tolerates the passive adversary to access any internal data of corrupted key escrow agents and the active adversary that can make corrupted servers to deviate from the protocol. The scheme is secure against threshold adaptive chosen-ciphertext attack. The formal proof of security is presented in the random oracle model, assuming the decision Bilinear Diffie-Hellman problem is computationally hard.

Provably secure non-interactive key distribution based on pairings

We define a security notion for non-interactive key distribution protocols. We identify an apparently hard computational problem related to pairings, the Bilinear Diffie–Hellman problem (BDH). After extending Sakai, Ohgishi, and Kasahara's pairing based protocol to a slightly more general setting, we show that breaking the system is polynomially equivalent to solving BDH in the random oracle model and thus establish a security proof.