Identity based cryptography from bilinear pairings

2004

The bilinear pairing such as Weil pairing or Tate pairing on elliptic and hyperelliptic curves have recently been found applications in design of cryptographic protocols. In this survey, we have tried to cover different cryptographic protocols based on bilinear pairings which possess, to the best of our knowledge, proper security proofs in the existing security models.

International Journal of Information and Education Technology, 2013

HAL (Le Centre pour la Communication Scientifique Directe), 2022

Identity Based Encryption is an approach to link the public key to an identity. It is an extremely useful asymmetric cryptography type in which public and private keys are computed from a known identifier such as an email address instead of being generated randomly. This allows more flexibility in managing ad-hoc public key encryption and ensuring secure communications. The aim of this work is to improve IBE scheme using the bilinear Tate pairing on genus two curves with ordinary Jacobian over large prime fields. We present a full description of functional IBE scheme using the optimization of the Tate pairing computations. The proposed application answers a question of Boneh and Franklin [2] about the possibility of using the Tate pairing in IBE schemes and represents the first IBE exploiting pairings in genus two. We provide a full description of a functional IBE scheme using the optimization of the Tate pairing computations.

Facta Universitatis, Series: Mathematics and Informatics, 2021

Identity-Based Encryption is a public key cryptosystem that uses the receiver identifier information such as email address, IP address, name and etc, to compute a public and a private key in a cryptosystem and encrypt a message. A message receiver can obtain the secret key corresponding with his privacy information from Private Key Generator and he can decrypt the ciphertext. In this paper, we review Boneh-Franklin’s scheme and use bilinear map and Weil pairing’s properties to propose an identity-based cryptography scheme based on isogeny of elliptic curves.

2004

Bilinear pairings have been intensively used in the design of cryptographic protocols during the last few years. For instance, short signatures and non-interactive key exchange protocols have been designed with them, and they appear as a key component for identity-based cryptography. Focusing on encryption and signature schemes built on bilinear pairings, we look at the security reductions of some known constructions. For any pair "scheme/security reduction", we deduce key sizes to securely implement the schemes. It turns out that some important protocols in the literature appear to be not as efficient as one would wish, due to the lack of tightness of their security reductions. Finally, we summarize current trends to obtain tight security reductions and suggest some open problems.

2004

In Asiacrypt2001, Boneh, Lynn, and Shacham [8] proposed a short signature scheme (BLS scheme) using bilinear pairing on certain elliptic and hyperelliptic curves. Subsequently numerous cryptographic schemes based on BLS signature scheme were proposed. BLS short signature needs a special hash function . This hash function is probabilistic and generally inefficient. In this paper, we propose a new short signature scheme from the bilinear pairings that unlike BLS, uses general cryptographic hash functions such as SHA-1 or MD5, and does not require special hash functions. Furthermore, the scheme requires less pairing operations than BLS scheme and so is more efficient than BLS scheme. We use this signature scheme to construct a ring signature scheme and a new method for delegation. We give the security proofs for the new signature scheme and the ring signature scheme in the random oracle model.

Advances in Neural Information Processing Systems. …, 2004

RSA is a key cryptography technique and provides various interfaces for the applied software in real-life scenarios. Although some good results were achieved in speeding up the computation of pairing function in recent years, the computation cost of the pairings is much higher than that of the exponentiation in a RSA group. So it is still interesting to design efficient cryptosystems based on RSA primitive. A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer within a given context. Most identity based proxy signature schemes currently known employ bilinear pairings. In this paper, an identity based proxy ring signature (IBPS) scheme from RSA without pairings is constructed, and the security is proved under the random oracle model.

2006 2nd International Conference on Information & Communication Technologies, 2006

Proxy signature schemes allow a proxy signer to generate a proxy signature on behalf of an original signer. In this paper we propose an Identity-based proxy signature scheme from bilinear pairings. In comparison with the Xu et al's scheme, our scheme is more efficient in computation and requires fewer pairing operations especially in verification phase.

Journal of Cryptology, 2004

Pairing-based cryptosystems rely on the existence of bilinear, nondegenerate, efficiently computable maps (called pairings) over certain groups. Currently, all such pairings used in practice are related to the Tate pairing on elliptic curve groups whose embedding degree is large enough to maintain a good security level, but small enough for arithmetic operations to be feasible. In this paper we describe how to construct ordinary (non-supersingular) elliptic curves containing groups with arbitrary embedding degree, and show how to compute the Tate pairing on these groups efficiently.

We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational Diffie-Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.

Applied Mathematics and Computation, 2005

Since Boneh and Franklin gave the first feasible solutions for identity-based encryption using Weil pairing on elliptic curves, many identity-based key agreement protocols and signature schemes using bilinear pairing have been suggested. As argued in [8], secure and efficient key agreement protocols should provide certain security attributes and have minimal number of passes. Until now, there is no secure two-pass ID-based authenticated key agreement protocol satisfying perfect forward secrecy. Here, we propose a few ID-based authenticated key agreement protocols based on a bilinear pairing. Our final protocol is a two-pass authenticated key agreement protocol with required security attributes and minimal number of passes.

Arxiv preprint cs/0504097, 2005

Lecture Notes in Computer Science, 2013

We present efficient Identity-Based Encryption (IBE) and signature schemes under the Symmetric External Diffie-Hellman (SXDH) assumption in bilinear groups. In both the IBE and the signature schemes, all parameters have constant numbers of group elements, and are shorter than those of previous constructions based on Decisional Linear (DLIN) assumption. Our constructions use both dual system encryption (Waters, Crypto '09) and dual pairing vector spaces (Okamoto and Takashima, Pairing '08, Asiacrypt '09). Specifically, we show how to adapt the recent DLIN-based instantiations of Lewko (Eurocrypt '12) to the SXDH assumption. To our knowledge, this is the first work to instantiate either dual system encryption or dual pairing vector spaces under the SXDH assumption.

The ISC International Journal of Information Security, 2023

In the last two decades bilinear pairings have found many applications in cryptography. Meanwhile identity-based cryptosystems based on bilinear pairings have received particular attention. The IEEE, IETF, and ISO organizations have been working on standardization of pairing-based cryptographic schemes. The Boneh-Franklin identity-based encryption and Sakai-Kasahara identity-based signature are the most well-known identity-based schemes that have been standardized. So far, various schemes have been proposed to reduce the computational overhead of pairing operations. All these schemes are trying to outsource pairing operations in a secure manner. But besides pairing operations, there are other basic and costly operations in pairing-based cryptography and identity-based schemes, including scalar multiplication on elliptic curves. In this research, we outsource the Boneh-Franklin encryption in a more secure and efficient (in terms of computational and communication complexity) way than existing schemes. Also we outsource the BLMQ signature (based on Sakai-Kasahara) scheme for the first time. The proposed schemes are secure in the OMTUP model. Also, unlike previous schemes, we considered communication channels insecure. Moreover, compared with the trivial solution which outsources every single operation (such as pairing, scalar multiplication and modular exponentiation) as a separate subroutine, our schemes offer less complexity by seamlessly outsourcing the whole encryption scheme for the first time. https://www.isecure-journal.com/article_170579.html