• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.303-309
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• 2009

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computational Diffie-Hellman assumption implies the bilinear Diffie-Hellman assumption or the general inversion assumption. Secondly, we show that a cryptographic useful self-bilinear map does not exist. If a self-bilinear map exists, it might be used as a building block for several cryptographic applications such as a multilinear map. As a corollary, we show that a fixed inversion of a bilinear map with homomorphic property is impossible. Finally, we remark that a self-bilinear map proposed in [7] is not essentially self-bilinear.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.5
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• pp.165-176
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• 2004

Al-Riyami and Paterson$^{[1]}$ suggested the new public key paradigm which is called the certificateless public key system. This system takes the advantages of both traditional PKC and ID-based PKC. It does not require the use of certificates of the public key and does not have the key escrow problem caused from the ID-based cryptosystem. In this paper, we propose an efficient certificateless public key encryption scheme which satisfies mutual authentication. The security of our protocol is based on the hardness of two problems; the computational Diffie-Hellman problem(CDHP) and the bilinear Diffie-Hellman problem(BDHP). We also give a formal security model for both confidentiality and unforgeability, and then show that our scheme is probably secure in the random oracle model.

• Journal of KIISE:Information Networking
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• v.31 no.6
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• pp.545-555
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• 2004

Proxy signature scheme allow a designated proxy person to sign a message on behalf of the original signer. Partially blind signature scheme allows the signer to insert non-removable common information into his blind signature. Proxy signature and partially blind signature are very important technologies in secure e-commerce. In this paper we propose new proxy signature scheme and ID-based partially blind signature scheme using bilinear pairing. further combining them, we propose a proxy partially blind signature scheme. The security of our schemes relies on the hardness of Computational Diffie-Hellman Problem. If we removing common information form propose ID-based partially blind signature scheme and proxy partially blind signature scheme, then they become variants of ID-based blind signature scheme and proxy blind signature scheme of Zhangs respectively.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.11
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• pp.967-969
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• 2013

In this paper, we propose an efficient mult-signature scheme based on a bilinear mapping for shared data in the cloud and prove the security of the proposed scheme using the difficulty of the computational Diffie-Hellman problem. For verification, the scheme is using the sum of the hash values of stored data rather than the entire data, which makes it feasible to reduce the size of the downloaded data.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.201-208
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• 2010

We propose a new notion of metered signatures. Metered signature is an extension of k-times signatures in which a signer can generate only k signatures. However, the restriction of metered signatures can be more elaborate: It can be used k-times every day or to preserve the order of signed messages in some applications. Any violation of this regulation reveals a secret key or the signature on a predetermined message. The applications includes proxy signatures, limited free downloads, and the rating web site. We give two instances of metered signatures: One is based on the computational Diffie-Hellman problem (CDHP) using a bilinear map and the other is based on the RSA problem. In both schemes, the signature and certificate size and the verification cost are constant with respect to k. Further, we show that the proposed metered signatures admit batch verification of many signatures almost at one verification cost with small security loss.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.8
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• pp.1972-1988
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• 2013

In order to deal with key exposure problem, we introduce forward secure technique into certificateless proxy signature scheme, and propose the formal definition and security model of the forward secure certificateless proxy signature. Our security model takes into account the super adversary in certificateless signature. Furthermore, we present a construction of forward secure certificateless proxy signature scheme with bilinear maps. Based on the difficulty of computational Diffie-Hellman problem, we prove the scheme is secure against chosen message attack in the random oracle model. Finally, we analyze efficiency of the proposed scheme.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.6
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• pp.1109-1122
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• 2016

Certificateless public key cryptography is a technique that can solve the certificate management problem of a public key cryptosystem and clear the key escrow issue of ID-based cryptography using the public key in user ID. Although the studies were actively in progress, many existing schemes have been designed without taking into account the safety of the secret value with the decryption key exposure attacks. If previous secret values and decryption keys are exposed after replacing public key, a valid private key can be calculated by obtaining the partial private key corresponding to user's ID. In this paper, we propose a new security model which ensures the security against the key exposure attacks and show that several certificateless public key encryption schemes are insecure in the proposed security model. In addition, we design a certificateless public key encryption scheme to be secure in the proposed security model and prove it based on the DBDH(Decisional Bilinear Diffie-Hellman) assumption.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.2
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• pp.881-896
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• 2016

Certificate-based cryptography is a useful public key cryptographic primitive that combines the merits of traditional public key cryptography and identity-based cryptography. It not only solves the key escrow problem inherent in identity-based cryptography, but also simplifies the cumbersome certificate management problem in traditional public key cryptography. In this paper, by giving a concrete attack, we first show that the certificate-based encryption scheme without bilinear pairings proposed by Yao et al. does not achieve either the chosen-ciphertext security or the weaker chosen-plaintext security. To overcome the security weakness in Yao et al.'s scheme, we propose an enhanced certificate-based encryption scheme that does not use the bilinear pairings. In the random oracle model, we formally prove it to be chosen-ciphertext secure under the computational Diffie-Hellman assumption. The experimental results show that the proposed scheme enjoys obvious advantage in the computation efficiency compared with the previous certificate-based encryption schemes. Without costly pairing operations, it is suitable to be employed on the computation-limited or power-constrained devices.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.6
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• pp.149-161
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• 2003

Partially blind signature scheme allows the signer to insert non-removable common information into his blind signature. Blind signatures providing with both users privacy and data authenticity are one of key parts of information systems, such anonymous electronic cash and electronic voting as typical examples. Partially blind signature, with which all expired e-cash but for still-alive can be removed from the banks database, copes well with the problem of unlimited growth of the banks' database in an electronic cash system. In this paper we propose an efficient ID-based partially blind signature scheme using the Weil-pairing on Gap Diffie-Hellman group. The security of our scheme relies on the hardness of Computational Diffie-Hellman Problem. The proposed scheme provides higher efficiency than existing partially blind signature schemes by using three-pass protocol between two participants, the signer and requesters also by reducing the computation load. Thus it can be efficiently used in wireless environment.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.46 no.1
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• pp.46-55
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• 2009

We study the problem of searching documents containing each of several keywords (conjunctive keyword search) over encrypted documents. A conjunctive keyword search protocol consists of three entities: a data supplier, a storage system such as database, and a user of storage system. A data supplier uploads encrypted documents on a storage system, and then a user of the storage system searches documents containing each of several keywords. Recently, many schemes on conjunctive keyword search have been suggested in various settings. However, the schemes require high computation cost for the data supplier or user storage. Moreover, up to now, their securities have been proved in the random oracle model. In this paper, we propose efficient conjunctive keyword search schemes over encrypted documents, for which security is proved without using random oracles. The storage of a user and the computational and communication costs of a data supplier in the proposed schemes are constant. The security of the scheme relies only on the hardness of the Decisional Bilinear Diffie-Hellman (DBDH) problem.