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Sender and Recipient Un-restricted, Non-interactive Group Key Exchange for Dynamic Group with Low-quality Network

Rui Zhang, Lei Zhang, Yihuai Liang, Jiahuai Mao, Jin Zhou

Published Jun 22, 2026• 0 citations
Publisher

Abstract

Abstract Non-interactive group key exchange is a fundamental primitive for establishing secure communication channels in multi-party settings. However, existing protocols usually rely on computationally expensive tools, such as multi-linear maps and indistinguishability obfuscation, or lack efficient support for dynamic groups. To address these limitations, we propose a secure and efficient non-interactive group key exchange protocol built upon bilinear maps, which offers the following advantages over existing solutions. First, our protocol suits well for dynamic groups by enabling non-interactive key updates to accommodate frequent membership changes. Second, it exhibits two desirable features for distributed applications: sender un-restriction, which permits any party to send a message, and recipient un-restriction, which allows a sender to select an arbitrary subset of members as recipients. Furthermore, our protocol generates constant-size ciphertexts, enhancing its efficiency and scalability. We formally prove that our protocol achieves fully collusion-resistance in the standard model under the k-Bilinear Diffie-Hellman Exponent (k-BDHE) assumption. Performance analysis confirms the protocol's practical efficiency.

DOI
10.21203/rs.3.rs-9547370/v1

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Abstract Non-interactive group key exchange is a fundamental primitive for establishing secure communication channels in multi-party settings. However, existing protocols usually rely on computationally expensive tools, such as multi-linear maps and indistinguishability obfuscation, or lack efficient support for dynamic groups. To address these limitations, we propose a secure and efficient non-interactive group key exchange protocol built upon bilinear maps, which offers the following advantages over existing solutions. First, our protocol suits well for dynamic groups by enabling non-interactive key updates to accommodate frequent membership changes. Second, it exhibits two desirable features for distributed applications: sender un-restriction, which permits any party to send a message, and recipient un-restriction, which allows a sender to select an arbitrary subset of members as recipients. Furthermore, our protocol generates constant-size ciphertexts, enhancing its efficiency and scalability. We formally prove that our protocol achieves fully collusion-resistance in the standard model under the k-Bilinear Diffie-Hellman Exponent (k-BDHE) assumption. Performance analysis confirms the protocol's practical efficiency.
Non-interactive key exchange (NIKE) enables two or multiple parties (just knowing the public system parameters and each other's public key) to derive a (group) session key without the need for interaction. Recently, NIKE in multi-party settings has been attached importance. However, we note that most existing multi-party NIKE protocols, underlying costly cryptographic techniques (i.e., multilinear maps and indistinguishability obfuscation), lead to high computational costs once employed in practice. Therefore, it is a challenging task to achieve multi-party NIKE protocols by using more practical cryptographic primitives. In this paper, we propose a secure and efficient NIKE protocol for secure communications in dynamic groups, whose construction only bases on bilinear maps. This protocol allows multiple parties to negotiate asymmetric group keys (a public group encryption key and each party's decryption key) without any interaction among one another. Additionally, the protocol supports updating of group keys in an efficient and non-interactive way once any party outside a group or any group member joins or leaves the group. Further, any party called a sender (even outside a group) intending to connect with some or all of group members called receivers in a group, just needs to generate a ciphertext with constant size under the public group encryption key, and only the group member who is the real receiver can decrypt the ciphertext to obtain the session key. We prove our protocol captures the correctness and indistinguishability of session key under k-Bilinear Diffie-Hellman exponent (k-BDHE) assumption. Efficiency evaluation shows the efficiency of our protocol.
Two novel constructions of one out of n oblivious transfer protocols from bilinear maps between groups are proposed. The protocols satisfy the category of non-interactive, mean that any sender S can obliviously transfer some secret(s) to a receiver R, but R does not send any messages back to S. The choice of a receiver is unconditionally secure. A sender's secrecy is guaranteed if the receiver is semi-honest in a standard model since the decision bilinear Diffie-Hellman problem is hard and the sender's secrecy is achieved when the receiver is a malicious party in a random oracle model since the bilinear Diffie-Hellman problem assumption holds. When a sender is a cheating party, the receiver will detect him/her and halt the protocol. A precise proof of the security of the protocols is presented.
Group-oriented applications generally support communications for multiple entities (e.g., users and/or devices) through open networks. Typical requirements of group communications include secrecy, authentication, sender non-repudiation, and sender privacy. However, conventional approaches such as group key agreement and broadcast encryption are generally not designed to achieve all these requirements simultaneously or efficiently. In this article, we propose a one-round dynamic authenticated asymmetric group key agreement with sender non-repudiation and privacy (DAAGKAwSNP) protocol. A key building block of our DAAGKAwSNP protocol is our proposed batch multi-signature scheme with strong unforgeability. We prove that the DAAGKAwSNP protocol achieves secrecy under chosen ciphertext attacks – CCA, assuming the intractability of the computational Diffie-Hellman and k-Bilinear Diffie-Hellman exponent problem. We also evaluate DAAGKAwSNP’s performance to demonstrate its utility.
Modern collaborative and group-oriented applications typically involve communications over open networks. Given the openness of today's networks, communications among group members must be secure and, at the same time, efficient. Group key agreement (GKA) is widely employed for secure group communications in modern collaborative and group-oriented applications. This paper studies the problem of GKA in identity-based cryptosystems with an emphasis on round-efficient, sender-unrestricted, member-dynamic, and provably secure key escrow freeness. The problem is resolved by proposing a one-round dynamic asymmetric GKA protocol which allows a group of members to dynamically establish a public group encryption key, while each member has a different secret decryption key in an identity-based cryptosystem. Knowing the group encryption key, any entity can encrypt to the group members so that only the members can decrypt. We construct this protocol with a strongly unforgeable stateful identity-based batch multisignature scheme. The proposed protocol is shown to be secure under the k -bilinear Diffie-Hellman exponent assumption.
Group key exchange protocols play main role in group applications such as computer networks, telecommunication and military systems. Given the wide range of usage of group applications, research and design of these protocols can play an important role in securing international exchanges, trade and military issues. Most existing group key exchange protocols establish multi-party or group key exchange protocols based on extending the two party well known Diffie- Hellman key exchanges. The security of these protocols is based on this assumption that difficulty of solving group Dif- fie-Hellman problem can be reduced to the difficulty of two party Diffie-Hellman problems. In spite of this assumption, Group key exchanges are not simply extension of two party protocols. In fact there are many differences and challenges that must be considered in design and implementation of these protocols. This difference is due to essential difference between peer to peer communication and group communication. In group communication in addition to considering the main goal e.g. obtaining group session key, consideration of group member changing is important too. In this paper, a Dynamic ID-based Group Key Agreement protocol based on Weil pairing is proposed. This complete ternary tree struc- ture is used and dynamic changes in group are considered too. Finally we show that the proposed protocol is more effi- cient than other protocols with similar structure and also satisfies all known security requirements .
Nowadays many crucial network applications rely on the existence of a confidential channel established by authenticated key exchange (AKE) protocols over public networks.With the rapid development of cyber technology, novel attacks to cryptosystem emerge in an endless stream.This has also led to the development of AKE solutions to provide increasingly stronger security guarantees.In this thesis we focus on provision of practical constructions for AKE protocols which are provably secure in a strong sense without resorting to random oracles.We first we present three new efficient compilers to generically turn passively secure key exchange protocols (KE) into authenticated key exchange protocols (AKE) where security also holds in the presence of active adversaries.Our compilers are not only a useful tool for the design of new AKE systems with many additional security properties in a modular and less error-prone fashion, but they also help to relax the assumptions on existing, practical key exchange mechanisms which are not known to be provably secure AKE protocols.Security of our compilers is shown in a strong modified CK model where the adversary is allowed to reveal either long-term secret key or state information of the protocol participants.On the second, we study the open problem on constructing eCK secure two party AKE protocol without random oracles and NAXOS trick.A generic construction satisfying those requirements is given based on well-known cryptographic primitives following the guideline of efficiency.Then a concrete protocol is proposed which is the first eCK secure protocol in the standard model under both standard assumptions and post-specified peer setting (i.e.without knowing any cryptographic information about its communication peer).Both proposed schemes can be more efficiently implemented with secure device than previous works which are eCK secure in the standard model, where the secure device might be normally used to store the long-term private key and to implement codes of protocol which need to be resilience of state leakage.Finally, we generalize our one-round two party AKE construction to group case that yields an efficient tripartite AKE protocol based on bilinear maps and a candidate group AKE protocol (with more than three members) based on multilinear maps.Up to now they are the first solutions which can be proved secure in the g-eCK model without random oracles.Meanwhile we make first step to show how to simplify the security proof for one-round group AKE under g-eCK model.i