• Journal of KIISE:Information Networking
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• v.30 no.6
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• pp.720-728
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• 2003

Blind signature is such a signature scheme that conceals the contents of signature itself and who is the user of the signature make user's anonymity possible. For this reason, they are used in security services such as electronic cashes and electronic votes in which the behavior of actor should not be exposed. In this paper we propose an ID-based blind signature scheme from Gap Diffie-Hellman group. Its security is based on the hardness of Computational Diffie-Hellman Problem. Proposed scheme efficiently improve against existing blind signature scheme by using two-pass protocol between two users and by reducing computation process. Therefore it can be used efficiently in wireless PKI environment.

• 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 applied mathematics & informatics
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• v.39 no.1_2
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• pp.93-103
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• 2021

In this paper I am considering several cryptological threads. The problem of the RSA cipher, like the Diffie-Hellman protocol, is the use of finite sets. In this paper, I generalize the RSA cipher and DH protocol for infinite sets using monoids. In monoids we can not find the inverse, which makes it difficult. In the second part of the paper I show the applications in cryptology of polynomial composites and monoid domains. These are less known structures. In this work, I show different ways of encrypting messages based on infinite sets.

• 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.

• 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 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.245-253
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• 2009

A new hard problem called the vector decomposition problem (VDP) was recently proposed by Yoshida et al., and it was asserted that the VDP is at least as hard as the computational Diffie-Hellman problem (CDHP) under certain conditions. Kwon and Lee showed that the VDP can be solved in polynomial time in the length of the input for a certain basis even if it satisfies Yoshida's conditions. Extending our previous result, we provide the general condition of the weak instance for the VDP in this paper. However, when the VDP is practically used in cryptographic protocols, a basis of the vector space ${\nu}$ is randomly chosen and publicly known assuming that the VDP with respect to the given basis is hard for a random vector. Thus we suggest the type of strong bases on which the VDP can serve as an intractable problem in cryptographic protocols, and prove that the VDP with respect to such bases is difficult for any random vector in ${\nu}$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.3
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• pp.27-33
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• 2007

Recently, a new hard problem on a two dimensional vector space called vector decomposition problem (VDP) was proposed by M. Yoshida et al. and proved that it is at least as hard as the computational Diffe-Hellman problem (CDHP) on a one dimensional subspace under certain conditions. However, in this paper we present the VDP relative to a specific basis can be solved in polynomial time although the conditions proposed by M. Yoshida on the vector space are satisfied. We also suggest strong instances based on a certain type basis which make the VDP difficult for any random vector relative to the basis. Therefore, we need to choose the basis carefully so that the VDP can serve as the underlying intractable problem in the cryptographic protocols.

• 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.