• ETRI Journal
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• 제22권4호
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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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• 제8권2호
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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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• 제14권11호
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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.

• 한국군사과학기술학회지
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• 제12권4호
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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.

• 한국정보통신학회논문지
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• 제10권8호
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• pp.1443-1448
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• 2006

컴퓨터와 네트워크의 보급이 일반화되면서 인터넷을 통한 정보 전달이 일상생활처럼 되고 있다. 기존에는 정보를 전달하기 위한 방법이 주로 전자메일에 한정되어 있던 것에 반해, 요즘은 좀 더 즉각적으로 메시지를 전달해주는 메신저를 많이 사용하고 있다. 현재 사용되고 있는 대부분의 메신저는 자료의 효과적인 관리를 위한 통신의 주체가 되는 각각의 에이젼트들간의 통신과 서버와 에이젼트의 통신에 있어 악의적인 침입에 의한 정보누출이 문제가 되고 있다. 본 논문에서는 메신저의 안전한 통신을 위해 PKI를 이용한 ElGamal 방식의 ECC 이용하여 최대한 안전성이 확보될 수 있고 사용자그룹 단위의 암호화를 위해 그룹별로 타원곡선과그 위에 있는 임의의 점을 선택하여 다른 그룹과 구별할 수 있는 안전한 메신저 시스템을 설계하였다.

• 대한수학회지
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• 제50권2호
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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.

• 정보보호학회논문지
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• 제9권2호
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• pp.83-92
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• 1999

암호를 사용함으로써 정보를 위.변조나 노출 위협으로부터 보호할 수 있지만, 암호의 잘못된 사용은 몇 가지 문제점을 발생시킬 수 있다. 만약 키가 손상되면 암호의 적법한 소유자조차도 암호문을 해독할 수 없으며, 범죄 등의 목적에 암호가 사용되었을 경우, 수사 기관이 수사에 어려움을 겪을 수 있다. 이러한 문제점을 해결하기 위해 키 또는 메시지를 복구할 수 있도록 키를 신뢰기관에 위탁하는 키 위탁(key escrow) 방식이 제안되었다. 키 위탁은 유사시 키 복구를 보장하면서 동시에 사용자의 사생활을 침해해서는 안된다. 본 논문에서는 키 위탁 시스템이 가져야할 요구사항을 도출하고, EIGamal 암호 시스템에 기반한 새로운 키 위탁 방식을 제안한다. 제안 방식은 도청기한의 제한, 키의 복구에 관련된 부정 방지와 이에 대한 사용자의 shadow 공개키 생성 방지 등의 속성을 갖는 새로운 키위탁 방식이다. 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.

• 전기전자학회논문지
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• 제23권4호
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• pp.1321-1327
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• 2019

본 논문에서는 GF(p) 상에서 모듈러 제곱근 (MSQR) 연산의 효율적인 하드웨어 구현에 대해 기술한다. MSQR 연산은 타원곡선 기반의 EC-ElGamal 공개키 암호를 위해 평문 메시지를 타원곡선 상의 점으로 매핑하기 위해 필요하다. 본 논문의 방법은 NIST 표준으로 규정된 5가지 크기의 GF(p) 타원곡선을 지원하며, 192-비트, 256-비트, 384-비트 그리고 521-비트 크기의 Kobliz 곡선과 슈도 랜덤 곡선들은 모듈러 값의 특성을 기반으로 오일러 판정법을 적용하고, 224-비트 크기의 경우에는 Tonelli-Shanks 알고리듬을 간략화시켜 적용하였다. 제안된 방법을 ECC 프로세서의 32-비트 데이터 패스를 갖는 유한체 연산회로와 메모리 블록을 이용하여 구현하였으며, FPGA 디바이스에 구현하여 하드웨어 동작을 검증하였다. 구현된 회로가 50 MHz 클록으로 동작하는 경우에, 224-비트 슈도 랜덤 곡선의 경우에는 MSQR 계산에 약 18 ms가 소요되고, 256-비트 Kobliz 곡선의 경우에는 약 4 ms가 소요된다.

• 대한수학회보
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• 제50권6호
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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.

• 한국군사과학기술학회지
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• 제13권4호
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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.