• ETRI Journal
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• v.22 no.4
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• pp.25-31
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• 2000

Design of secure and efficient public-key encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as ElGamal-type encryption schemes are concerned, some variants of the original ElGamal encryption scheme based on weaker computational assumption have been proposed: Although security of the ElGamal variant of Fujisaki-Okamoto public -key encryption scheme and Cramer and Shoup's encryption scheme is based on the Decisional Diffie-Hellman Assumption (DDH-A), security of the recent Pointcheval's ElGamal encryption variant is based on the Computational Diffie-Hellman Assumption (CDH-A), which is known to be weaker than DDH-A. In this paper, we propose new ElGamal encryption variants whose security is based on CDH-A and the Elliptic Curve Computational Diffie-Hellman Assumption (EC-CDH-A). Also, we show that the proposed variants are secure against the adaptive chosen-ciphertext attack in the random oracle model. An important feature of the proposed variants is length-efficiency which provides shorter ciphertexts than those of other schemes.

• Journal of Information Processing Systems
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• v.8 no.2
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• pp.375-388
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• 2012

PVSS stands for publicly verifiable secret sharing. In PVSS, a dealer shares a secret among multiple share holders. He encrypts the shares using the shareholders' encryption algorithms and publicly proves that the encrypted shares are valid. Most of the existing PVSS schemes do not employ an ElGamal encryption to encrypt the shares. Instead, they usually employ other encryption algorithms like a RSA encryption and Paillier encryption. Those encryption algorithms do not support the shareholders' encryption algorithms to employ the same decryption modulus. As a result, PVSS based on those encryption algorithms must employ additional range proofs to guarantee the validity of the shares obtained by the shareholders. Although the shareholders can employ ElGamal encryptions with the same decryption modulus in PVSS such that the range proof can be avoided, there are only two PVSS schemes based on ElGamal encryption. Moreover, the two schemes have their drawbacks. One of them employs a costly repeating-proof mechanism, which needs to repeat the dealer's proof at least scores of times to achieve satisfactory soundness. The other requires that the dealer must know the discrete logarithm of the secret to share and thus weakens the generality and it cannot be employed in many applications. A new PVSS scheme based on an ElGamal encryption is proposed in this paper. It employs the same decryption modulus for all the shareholders' ElGamal encryption algorithms, so it does not need any range proof. Moreover, it is a general PVSS technique without any special limitation. Finally, an encryption-improving technique is proposed to achieve very high efficiency in the new PVSS scheme. It only needs a number of exponentiations in large cyclic groups that are linear in the number of the shareholders, while all the existing PVSS schemes need at least a number of exponentiations in large cyclic groups that are linear in the square of the number of the shareholders.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.11
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• pp.4522-4536
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• 2020

Nowadays, cloud is the fastest emerging technology in the IT industry. We can store and retrieve data from the cloud. The most frequently occurring problems in the cloud are security and privacy preservation of data. For improving its security, secret information must be protected from various illegal accesses. Numerous traditional cryptography algorithms have been used to increase the privacy in preserving cloud data. Still, there are some problems in privacy protection because of its reduced security. Thus, this article proposes an ElGamal Elliptic Curve (EGEC) Homomorphic encryption scheme for safeguarding the confidentiality of data stored in a cloud. The Users who hold a data can encipher the input data using the proposed EGEC encryption scheme. The homomorphic operations are computed on encrypted data. Whenever user sends data access permission requests to the cloud data storage. The Cloud Service Provider (CSP) validates the user access policy and provides the encrypted data to the user. ElGamal Elliptic Curve (EGEC) decryption was used to generate an original input data. The proposed EGEC homomorphic encryption scheme can be tested using different performance metrics such as execution time, encryption time, decryption time, memory usage, encryption throughput, and decryption throughput. However, efficacy of the ElGamal Elliptic Curve (EGEC) Homomorphic Encryption approach is explained by the comparison study of conventional approaches.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.4
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• pp.476-482
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• 2009

As a result from Hasse's theorem it is not always possible to share a common key between any two ECC public keys. Even though ECC algorithm is more efficient than any other Encryption's with respect to the encryption strength per bit, ECC ElGamal algorithm can not be used to distribute a common key to ECC PKI owners. Approaching mathematical ways in a practical situation, we suggest possible conditions to share a common key with ECC PKI's. Using computer experiments, we also show that these suggestions are right. In the conditions, we can distribute a common key to proper peoples with ECC ElGamal algorithm.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.8
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• pp.1443-1448
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• 2006

As computers and networks become popular, distributing information on the Internet is common in our daily life. In the past, e-mail has been the primary choice of exchanging information but messengers are gaining popularity abroad and domestically because of their nature of getting immediate responses. Information leakage by invasion that is enemy of evil in communication of communications division Server and Agent between each agents that become burden of communication for effective administration of data for most of existing messenger is becoming an issue. In this paper, we design a secure messenger system that could be obtained maximum security. It use ECC based on ElGamal methodology using PKI for secure communication. For the message encryption and decryption between the same group non, each group is kept distinct by drawing an elliptic curve and an arbitrary point is chosen on the curve.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.361-377
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• 2013

In this work we deal with the problem of how to squeeze multiple ciphertexts without losing original message information. To do so, we formalize the notion of decomposability for public-key encryption and investigate why adding decomposability is challenging. We construct an ElGamal encryption scheme over extension fields, and show that it supports the efficient decomposition. We then analyze security of our scheme under the standard DDH assumption, and evaluate the performance of our construction.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.2
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• pp.83-92
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• 1999

Cryptography techniques can prevent eavesdroppers from maliciously intercepting or modifying sensitive information. however misuses of encryption may cause other problems First if the encryption key is lost or damaged even an authorized access to the original data will be denied. Second criminals can prevent authorized law enforcement officers from examining the necessary information by using the strong encrypted data can provide solutions for the situations. In this paper we propose a new key escrow system based on the ElGamal cryptosystem. Our system provide time-bound eavesdropping under court authorized permission protect from trustee's cheating and prevent user's shadow public key generation.

• Journal of IKEEE
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• v.23 no.4
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• pp.1321-1327
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• 2019

This paper describes an efficient hardware implementation of modular square root (MSQR) computation over GF(p), which is the operation needed to map plaintext messages to points on elliptic curves for elliptic curve (EC)-ElGamal public-key encryption. Our method supports five sizes of elliptic curves over GF(p) defined by the National Institute of Standards and Technology (NIST) standard. For the Koblitz curves and the pseudorandom curves with 192-bit, 256-bit, 384-bit and 521-bit, the Euler's Criterion based on the characteristic of the modulo values was applied. For the elliptic curves with 224-bit, the Tonelli-Shanks algorithm was simplified and applied to compute MSQR. The proposed method was implemented using the finite field arithmetic circuit with 32-bit datapath and memory block of elliptic curve cryptography (ECC) processor, and its hardware operation was verified by implementing it on the Virtex-5 field programmable gate array (FPGA) device. When the implemented circuit operates with a 50 MHz clock, the computation of MSQR takes about 18 ms for 224-bit pseudorandom curves and about 4 ms for 256-bit Koblitz curves.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1799-1816
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• 2013

Privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose efficient PPMU protocols, using multiplicative homomorphic cryptosystem. The novelty of our protocol is to directly encrypt a polynomial by representing it by an element of an extension field. The resulting protocols consist of constant rounds and improve communication cost. We also prove the security of our protocol against malicious adversaries, in the random oracle model.

• Journal of the Korea Institute of Military Science and Technology
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• v.13 no.4
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• pp.627-634
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• 2010

In this paper we suggest a group key agreement protocol among a group consisting more than 3 PKIs. From an 128 bit message, we produce a group key to any length size using a hash function. With a computer experiment we found that PKI's encryption/decryption time is the most dominant part of this procedure and an 160 bit ECC PKI is the most efficient system for distributing an 128 bit message in practical level. We implement this procedure over an unsecure multi user chatting system which is an open software. And we also show that this suggestion could be practically used in military business without a hardware implementation.