Projecting bilinear pairings have frequently been used for designing cryptosystems since they were first derived from composite order bilinear groups. There have been only a few studies on the (im)possibility of projecting bilinear pairings. Groth and Sahai showed that projecting bilinear pairings can be achieved in the prime-order group setting. They constructed both projecting asymmetric bili...

Recent studyoncertificateless authenticated key agreement focuses on bilinear pairing-freecertificateless authenticated key agreement protocol. Yet it has got limitations in the aspect of computational amount.So it is important to reduce the number of the scalar multiplication over elliptic curve group in bilinear pairing-free protocols. This paper proposed a new bilinear pairing-freecertificat...

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.

The term “proxy multi-signature” refers to the situation in which a proxy signer is authorized to sign a message on behalf of a group of original signers. Combined with identity-based cryptography, we proposed an efficient identity-based proxy multi-signature scheme using cubic residues without bilinear pairing. Our scheme is secure against existential forgery on adaptive chosenmessage and iden...

Recently the bilinear pairing such as Weil pairing or Tate pairing on elliptic curves and hyperelliptic curves have been found various applications in cryptography. Several identity-based (simply ID-based) cryptosystems using bilinear pairings of elliptic curves or hyperelliptic curves were presented. Blind signature and ring signature are very useful to provide the user’s anonymity and the sig...

It has always been a critical issue to find efficient methods for fast revocation of a user’s identity in identity (ID)based cryptosystems. Unfortunately, none of the previous ID-based cryptography can find a practical way. Libert et al. and Baek et al. respectively propose an ID-based mediated encryption scheme based on the practical ID-based encryption scheme from bilinear pairing due to Bone...

Bilinear pairings have been used to design ingenious protocols for such tasks as one-round three-party key agreement, identity-based encryption, and aggregate signatures. Suitable bilinear pairings can be constructed from the Tate pairing for specially chosen elliptic curves. This article gives an introduction to the protocols, Tate pairing computation, and curve selection.

In this paper, we will implement a standard probabilistic method of computing bilinear pairings. We will compare its performance to a deterministic algorithm introduced in [5] to compute the squared Tate/Weil pairings which are claimed to be 20 percent faster than the standard method. All pairings will be evaluated over pairing-friendly ordinary elliptic curves of embedding degrees 8 and 10 and...

We investigate commitment schemes whose messages, keys, commitments, and decommitments are elements of bilinear groups, and whose openings are verified by pairing product equations. Such commitments facilitate efficient zero-knowledge proofs of knowledge of a correct opening. We show two lower bounds on such schemes: a commitment cannot be shorter than the message and verifying the opening in a...