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International Journal of Computers Communications & Control

An Authenticated Key Agreement Protocol Using Isogenies Between Elliptic Curves

Debiao He, Jianhua Chen, Hu Jin

Published Jun 1, 2011• 7 citations
Publisher

Abstract

All the current public-key cryptosystems will become insecure when size of a quantum register is sufficient. An authenticated key agreement protocol, which is against the attack of quantum computer, is proposed. The proposed protocol can provide the security properties known session key security, forward security, resistance to key-compromise impersonation attack and to unknown key-share attack, key control. We also prove its security in a widely accepted model.

DOI
10.15837/ijccc.2011.2.2174

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All the current public-key cryptosystems will become insecure when size of a quantum register is sufficient. An authenticated key agreement protocol, which is against the attack of quantum computer, is proposed. The proposed protocol can provide the security properties known session key security, forward security, resistance to key-compromise impersonation attack and to unknown key-share attack, key control. We also prove its security in a widely accepted model.
Authenticated key agreement protocol is designed to provide pair of parties communicating over an insecure network with a secure session key.However,most of the existing authenticated key agreement protocols are not designed for protecting privacy.We emphasize user's privacy properties in network services,in particular we stress anonymity and deniability.We specify the desired security properties of privacy-enhancing authentication key agreement protocols,i.e.mutual authentication,key control,key confirmation,session-key confidentiality,known-key security,forward secrecy,anonymity of user,forward anonymity of user,unlinkability,deniability.Based on elliptic curve cryptosystem we also propose a protocol which satisfies all the desired security properties.
Asymmetric group key agreement allows a group of users to negotiate a public encryption key that corresponds to several decryption keys, and each decryption key can only be computed by one group member. This novel notion ensures the confidentiality of communication among group members and allows any external entity to send messages to the group. However, the existing authenticated asymmetric group key agreement protocols are designed in identity-based cryptosystem or certificateless public key cryptosystem, which are not widely deployed. In this paper, we propose an efficient authenticated asymmetric group key agreement protocol. The protocol captures the security of secrecy, known-key security, key-compromise impersonation, unknown key-share and key control while being resistant to active attacks. The security of our protocol is reduced to the k-BDHE problem.
As the fundamental building block for secure communication in the open network, authenticated key agreement protocols are usually constructed in the public key setting. Certificateless public key cryptography combines the advantage of the identity-based public key cryptography (ID-PKC) and the traditional PKI. In this paper, we present a secure and efficient two-party authenticated key agreement protocol based on the efficient certificateless public key encryption scheme due to Cheng and Comley. Security analysis shows that it achieves perfect forward secrecy, PKG forward secrecy and almost all the other known security attributes for authenticated key agreement protocol, such as known-key secrecy, key-compromise impersonation resilience, unknown key-share resilience, known session-specific temporary information security, message independence and no key control. Compared to other comparable schemes, it is more secure and has nice efficiency.
Two-Party Authenticated key agreement protocol is essential for setting up the common session key for parties to establish secure channel for network communication in the open environment. Most of proposed schemes require expensive bilinear pairing operation and only provide limited security attributes. So such protocols are unsuitable for real-world applications that require stronger sense of secrecy. In this paper, we first analysis two schemes recently proposed by Cao etc., and then present a one-round ID-based authenticated key agreement protocol with more desired security attributes, which need no pairing operations while still achieve nice computational efficiency. These security attributes include known-key secrecy, perfect forward secrecy, PKG forward secrecy, key-compromise impersonation resilience, unknown key-share resilience and no key control. Moreover, it captures the enhanced security attributes known session-specific temporary key information secrecy, which means that even the ephemeral secret key were compromised, the adversary can hardly acquire the agreed session key.
We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These results were used as the motivation for De Feo, Jao and Pl\\^ut's construction of public key cryptosystems using supersingular elliptic curve isogenies. We extend their construction and show that isogenies between supersingular elliptic curves can be used as the underlying hard mathematical problem for other quantum-resistant schemes. For our second contribution, we propose is an undeniable signature scheme based on elliptic curve isogenies. We prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum algorithms are known. This proposal represents only the second known quantum-resistant undeniable signature scheme, and the first such scheme secure under a number-theoretic complexity assumption. Finally, we also propose a security model for evaluating the security of authenticated encryption schemes in the post-quantum setting. Our model is based on a combination of the classical Bellare-Namprempre security model for authenticated encryption together with modifications from Boneh and Zhandry to handle message authentication against quantum adversaries. We give a generic construction based on Bellare-Namprempre for producing an authenticated encryption protocol from any quantum-resistant symmetric-key encryption scheme together with any digital signature scheme or MAC admitting any classical security reduction to a quantum-computationally hard problem. We apply the results and show how we can explicitly construct authenticated encryption schemes based on isogenies.
Authenticated key agreement protocol is the fundamental building block for secure communication in the open network to ensure authentication and confidentiality of e-commerce and e-government applications. Certificateless public key cryptography combines the advantage of the identity-based public key cryptography (ID-PKC) and the traditional PKI. In this paper, we present a secure and efficient two-party authenticated key agreement protocol based on an efficient and secure certificateless public key encryption scheme. It achieves almost all the known security attributes for authenticated key agreement protocol, such as perfect forward secrecy, PKG forward secrecy, key-compromise impersonation resilience, unknown key-share resilience, message independence and no key control. Compared to other comparable schemes, it is more secure and has nice efficiency.