The client-server model is known to scale badly without redundant servers and caches. Information-Centric Networks (ICN) are an alternative designed to lessen that problem by distributing load to intermediary routers, lowering the bar to techniques only accessible to server farms. However, this seamlessness comes with its own set of problems. Communication security, by using a key per connection, prevents intermediaries from reading and thus caching content. We thus need to share a common key for larger groups of correspondents to be able to benefit from the advantages of ICN. This paper presents the algorithmic choices to establish such a group key, the adaptations made for ICN, its implementation, and the statistics backing its performances comparison with our baseline. The first results tend to show a performance improvement over the selected base algorithm.
Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm. A range of "post-quantum Diffie-Hellman" protocols have been proposed to mitigate this threat, including the Couveignes, Rostovtsev-Stolbunov, SIDH, and CSIDH schemes, all based on the combinatorial and number-theoretic structures formed by isogenies of elliptic curves. Pre-and post-quantum Diffie-Hellman schemes resemble each other at the highest level, but the further down we dive, the more differences emerge-differences that are…
This paper presents protocols for Kak's cubic transformation and proposes a modification to Diffie-Hellman key exchange protocol in order to achieve asymmetric oblivious exchange of keys.
In this paper, we proposed an authentication method according to Diffie-Hellman. First, we introduce different methods for authentication in IEEE.802.16 then we proposed an authentication method according to Diffie-Hellman and in the last we compare different methods for authentication to improve security in IEEE802.16e. CPN is a useful for simulation and compare protocol together so we use CPN tools in this paper.
We extend symbolic protocol analysis to apply to protocols using Diffie-Hellman operations. Diffie-Hellman operations act on a cyclic group of prime order, together with an exponentiation operator. The exponents form a finite field. This rich algebraic structure has resisted previous symbolic approaches. We work in an algebra defined by the normal forms of a rewriting theory (modulo associativity and commutativity). These normal forms allow us to define our crucial notion of indicator, a vector of integers that summarizes how many times each secret exponent appears in a message. We prove that …
An offline OpenPGP user might want to forward part or all of their email messages to third parties. Given that messages are encrypted, this requires transforming them into ciphertexts decryptable by the intended forwarded parties, while maintaining confidentiality and authentication. It is shown in recent lines of work that this can be achieved by means of proxy-re-encryption schemes, however, while encrypted email forwarding is the most mentioned application of proxy-re-encryption, it has not been implemented in the OpenPGP context, to the best of our knowledge. In this paper, we adapt the se…
The Diffie-Hellman key agreement protocol is based on taking large powers of a generator of a prime-order cyclic group. Some generators allow faster exponentiation. We show that to a large extent, using the fast generators is as secure as using a randomly chosen generator. On the other hand, we show that if there is some case in which fast generators are less secure, then this could be used by a malicious authority to generate a standard for the Diffie-Hellman key agreement protocol which has a hidden trapdoor.
We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol. Finally, to take full advantage of this procedure, we propose a group of matrices over a noncommutative ring as platform group
In this paper we study a key exchange protocol similar to Diffie-Hellman key exchange protocol using abelian subgroups of the automorphism group of a non-abelian nilpotent group. We also generalize group no.92 of Hall-Senior table \cite{halltable}, for arbitrary prime $p$ and show that for those groups, the group of central automorphisms commute. We use these for the key exchange we are studying.
Diffie-Hellman key-agreement and RSA cryptosystem are widely used to provide security in internet protocols. But both of the two algorithms are totally breakable using Shor's algorithms. This paper proposes two connected matrix-based key-agreements: (a) Diffie-Hellman Key-Agreement with Errors and (b) RSA-Resemble Key-agreement, which, respectively, bear resemblance to Diffie-Hellman key-agreement and RSA cryptosystem and thereby they gain some of the well-known security characteristics of these two algorithms, but without being subject to Shor's algorithms attacks. That is, the new schemes av…
This paper studies the relationships between the traditional Diffie-Hellman key agreement protocol and the identity-based (ID-based) key agreement protocol from pairings. For the Sakai-Ohgishi-Kasahara (SOK) ID-based key construction, we show that identical to the Diffie-Hellman protocol, the SOK key agreement protocol also has three variants, namely \emph{ephemeral}, \emph{semi-static} and \emph{static} versions. Upon this, we build solid relations between authenticated Diffie-Hellman (Auth-DH) protocols and ID-based authenticated key agreement (IB-AK) protocols, whereby we present two \emph{…
Enrich-by-need protocol analysis is a style of symbolic protocol analysis that characterizes all executions of a protocol that extend a given scenario. In effect, it computes a strongest security goal the protocol achieves in that scenario. CPSA, a Cryptographic Protocol Shapes Analyzer, implements enrich-by-need protocol analysis. In this paper, we describe how to analyze protocols using the Diffie-Hellman mechanism for key agreement (DH) in the enrich-by-need style. DH, while widespread, has been challenging for protocol analysis because of its algebraic structure. DH essentially involves fi…
The Internet of Things (IoT) is a fast growing field of devices being added to an interconnected environment in an abstract heterogeneous array of servers and other devices, called smart environments, ranging from private local (home) environments to nation-wide infrastructures, often accessible via unsecured wireless communications and information technologies, hence, massively open to attacks. In this paper we address some of issues that arise when connecting smart devices endowed with low computational capabilities to a home gateway via unsecured wireless communication channels, by using a …
Key establishment is one fundamental issue in wireless security. The widely used Diffie-Hellman key exchange is vulnerable to the man-in-the-middle attack. This paper presents a novel in-band solution for defending the man-in-the-middle attack during the key establishment process for wireless devices. Our solution is based on the insight that an attacker inevitably affects the link layer behavior of the wireless channel, and this behavior change introduced by the attacker can be detected by the legitimate users. Specifically, we propose a key exchange protocol and its corresponding channel acc…
Cryptography algorithm standards play a key role both to the practice of information security and to cryptography theory research. Among them, the MQV and HMQV protocols ((H)MQV, in short) are a family of (implicitly authenticated) Diffie-Hellman key-exchange (DHKE) protocols that are widely standardized and deployed. In this work, from some new perspectives and approaches and under some new design rationales and insights, we develop a new family of practical implicitly authenticated DHKE protocols, which enjoy notable performance among security, privacy, efficiency and easy deployment. We mak…
In 2004, Muzereau et al. showed how to use a reduction algorithm of the discrete logarithm problem to Diffie-Hellman problem in order to estimate lower bound on Diffie-Hellman problem on elliptic curves. They presented their estimates for various elliptic curves that are used in practical applications. In this paper, we show that a much tighter lower bound for Diffie-Hellman problem on those curves can be achieved, if one uses the multiplicative group of a finite field as an auxiliary group. Moreover, improved lower bound estimates on Diffie-Hellman problem for various recommended curves are a…
qDSA is a high-speed, high-security signature scheme that facilitates implementations with a very small memory footprint, a crucial requirement for embedded systems and IoT devices, and that uses the same public keys as modern Diffie--Hellman schemes based on Montgomery curves (such as Curve25519) or Kummer surfaces. qDSA resembles an adaptation of EdDSA to the world of Kummer varieties, which are quotients of algebraic groups by $\pm$1. Interestingly, qDSA does not require any full group operations or point recovery: all computations, including signature verification, occur on the quotient wh…
We offer a public key exchange protocol in the spirit of Diffie-Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This "nested structure" of the platform makes computation very efficient for legitimate parties. We discuss security of this scheme by addressing the Decision Diffie-Hellman (DDH) and Computational Diffie-Hellman (CDH) problems for our platform.
In this paper we present a new primitive for a key exchange protocol based on multivariate non-commutative polynomial rings, analogous to the classic Diffie-Hellman method. Our technique extends the proposed scheme of Boucher et al. from 2010. Their method was broken by Dubois and Kammerer in 2011, who exploited the Euclidean domain structure of the chosen ring. However, our proposal is immune against such attacks, without losing the advantages of non-commutative polynomial rings as outlined by Boucher et al. Moreover, our extension is not restricted to any particular ring, but is designed to …
We show how the Weil pairing can be used to evaluate the assigned characters of an imaginary quadratic order $\mathcal{O}$ in an unknown ideal class $[\mathfrak{a}] \in \mathrm{Cl}(\mathcal{O})$ that connects two given $\mathcal{O}$-oriented elliptic curves $(E, ι)$ and $(E', ι') = [\mathfrak{a}](E, ι)$. When specialized to ordinary elliptic curves over finite fields, our method is conceptually simpler and often somewhat faster than a recent approach due to Castryck, Sotáková and Vercauteren, who rely on the Tate pairing instead. The main implication of our work is that it breaks the decisiona…
This paper presents a new efficient protocol for k-out-of-n oblivious transfer which is a generalization of Parakh's 1-out-of-2 oblivious transfer protocol based on Diffie-Hellman key exchange. In the proposed protocol, the parties involved generate Diffie-Hellman keys obliviously and then use them for oblivious transfer of secrets.
We use matrices over bit strings as platforms for Diffie-Hellman-like public key exchange protocols. When multiplying matrices like that, we use Boolean OR operation on bit strings in place of addition and Boolean AND operation in place of multiplication. As a result, (1) computations with these matrices are very efficient; (2) standard methods of attacking Diffie-Hellman-like protocols are not applicable.
DHMark: Public-Key Watermarking for LLM-Generated Text via Diffie-Hellman-Guided Rejection Sampling
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）
In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we al…
Key-exchange protocols have been overlooked as a possible means for implementing oblivious transfer (OT). In this paper we present a protocol for mutual exchange of secrets, 1-out-of-2 OT and coin flipping similar to Diffie-Hellman protocol using the idea of obliviously exchanging encryption keys. Since, Diffie-Hellman scheme is widely used, our protocol may provide a useful alternative to the conventional methods for implementation of oblivious transfer and a useful primitive in building larger cryptographic schemes.
By analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman problem (CEDHP), and Decisional Entropoid Diffie-Hellman Problem (DEDHP). We post a conjecture that DEDHP is hard in Sylow $q$-subquasigroups. Next, we instantiate an entropoid Diffie-Hellman key exchange protocol. Due to the non-commutativity and non-associativity, the entropoid based cryptographic primitives are supposed to be resistant to quantum algorith…
Ephemeral Diffie-Hellman Over COSE (EDHOC) aims at being a very compact and lightweight authenticated Diffie-Hellman key exchange with ephemeral keys. It is expected to provide mutual authentication, forward secrecy, and identity protection, with a 128-bit security level.A formal analysis has already been proposed at SECRYPT '21, on a former version, leading to some improvements, in the ongoing evaluation process by IETF. Unfortunately, while formal analysis can detect some misconceptions in the protocol, it cannot evaluate the actual security level.In this paper, we study the last version. Wi…
In the spirit of Diffie Hellman the concept of a protocol algebra is introduced using certain amalgamated free product of Braid group B and Thompson group T together with a nilpotent subgroup H of index 2.
In 1976, Whitfield Diffie and Martin Hellman introduced the public key cryptography or asymmetric cryptography standards. Two years later, an asymmetric cryptosystem was published by Ralph Merkle and Martin Hellman called MH, based on a variant of knapsack problem known as the subset-sum problem which is proven to be NP-hard. Furthermore, over the last four decades, Metaheuristics have achieved a remarkable progress in solving NP-hard optimization problems. However, the conception of these methods raises several challenges, mainly the adaptation and the parameters setting. In this paper, we pr…
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This protocol can be based on any group or semigroup, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when this protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol…
A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compu…
Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $ϕ(n)$ is known. That is, given $g, g^x\in G_1$ and having oracle access to a `Diffie-Hellman Problem' solver with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $ϕ(n)$ is unknown (see conjuncture 3.1). We exploit this ``gap'' to construct a cryptosystem based on hidden order groups and present a pra…
We give a new two-pass authentication scheme, whichis a generalisation of an authentication scheme of Sibert-Dehornoy-Girault based on the Diffie-Hellman conjugacy problem. Compared to the above scheme, for some parameters it is more efficient with respect to multiplications. We sketch a proof that our authentication scheme is secure. We give a new key agreement protocols.
This paper addresses an interesting security problem in wireless ad hoc networks: the Dynamic Group Key Agreement key establishment. For secure group communication in an Ad hoc network, a group key shared by all group members is required. This group key should be updated when there are membership changes (when the new member joins or current member leaves) in the group. In this paper, We propose a novel, secure, scalable and efficient Region-Based Group Key Agreement protocol (RBGKA) for ad-hoc networks. This is implemented by a two-level structure and a new scheme of group key update. The ide…
Mobile Ad-hoc Network (MANET) is a collection of autonomous nodes or terminals which communicate with each other by forming a multi-hop radio network and maintaining connectivity in a decentralized manner. The conventional security solutions to provide key management through accessing trusted authorities or centralized servers are infeasible for this new environment since mobile ad hoc networks are characterized by the absence of any infrastructure, frequent mobility, and wireless links. We propose a hierarchical group key management scheme that is hierarchical and fully distributed with no ce…
Traditional key management techniques, such as public key cryptography or key distribution center (e.g., Kerberos), are often not effective for wireless sensor networks for the serious limitations in terms of computational power, energy supply, network bandwidth. In order to balance the security and efficiency, we propose a new scheme by employing LU Composition techniques for mutual authenticated pairwise key establishment and integrating LU Matrix with Elliptic Curve Diffie-Hellman for anonymous pathkey establishment. At the meantime, it is able to achieve efficient group key agreement and m…
This paper presents a novel pre-shared key (PSK) agreement scheme to establish a secure connection between a Wi-Fi client and access point (AP) without prior knowledge of a password. The standard IEEE 802.11 security method, Robust Security Network Association, widely known as Wi-Fi Protected Access (WPA) and WPA2, derives a shared cryptographic key if and only if a user provides an identical password which an AP possesses, causing ofinconvenience of obtaining and entering the password. In this paper, a proposed scheme, Secure Open AP (SOAP), adopts two public key algorithms, the elliptic curv…
Public key infrastructure (PKI) is the most widely used security mechanism for securing communications over the network. However, there are known performance issues, making it unsuitable for use in vehicular networks. In this paper, we propose a secure and authenticated key management protocol (SA-KMP) to overcome the shortcomings of the PKI. The SA-KMP scheme distributes repository containing the bindings of the en-tity's identity and its corresponding public key to each vehicle and road side unit. By doing so, certificate exchanges and certificate revocation lists are eliminated. Furthermore…
We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z_p. One of the (semi)groups is additive, the other one multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of Z_p is ever exposed, so all standard attacks on Diffie-Hellman-like protocols (including Shor's quantum algorithm attack) are not applicable.
To address known privacy problems with the EMV standard, EMVCo have proposed a Blinded Diffie-Hellman key establishment protocol, which is intended to be part of a future 2nd Gen EMV protocol. We point out that active attackers were not previously accounted for in the privacy requirements of this proposal protocol, and demonstrate that an active attacker can compromise unlinkability within a distance of 100cm. Here, we adopt a strong definition of unlinkability that does account for active attackers and propose an enhancement of the protocol proposed by EMVCo. We prove that our protocol does s…
We present an elementary proof of the group properties of the elliptic curve known as "Curve25519", as a component of a comprehensive proof of correctness of a hardware implementation of the associated Diffie-Hellman key agreement algorithm. The entire proof has been formalized and mechanically verified with ACL2, and is computationally surveyable in the sense that all steps that require mechanical support are presented in such a way that they may readily reproduced in any suitable programming language.
A recently proposed authenticated key agreement protocol is shown to be insecure. In particular, one of the two parties is not authenticated, allowing an active man in the middle opponent to replay old messages. The protocol is essentially an authenticated Diffie-Hellman key agreement scheme, and the lack of authentication allows an attacker to replay old messages and have them accepted. Moreover, if the ephemeral key used to compute a protocol message is ever compromised, then the key established using the replayed message will also be compromised. Fixing the problem is simple - there are man…
Limited resources (such as energy, computing power, storage, and so on) make it impractical for wireless sensor networks (WSNs) to deploy traditional security schemes. In this paper, a hierarchical key management scheme is proposed on the basis of identity-based encryption (IBE).This proposed scheme not only converts the distributed flat architecture of the WSNs to a hierarchical architecture for better network management but also ensures the independence and security of the sub-networks. This paper firstly reviews the identity-based encryption, particularly, the Boneh-Franklin algorithm. Then…
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new homomorphic public-key cryptosystem. They rely on difficulty of the conjugacy and membership problems for subgroups of a given group. To support these and other known cryptographic schemes we present a general technique to produce a family of instances being matrix groups (over finite commutative rings) which play a role for these schemes similar to the groups $Z\_n^*…
The widespread use of wireless sensor networks (WSNs) that are consisted of resource-constrained sensor nodes in communication with gateways in open-space environments and industries has highlighted the need for a secure yet fast communication protocol between users, gateways, and sensor nodes. Due to the properties of the network, elliptic-curve cryptography seems to be the most viable choice as it requires fewer resources than most other options. In this paper, we analyze the protocol suggested by Moghadam et al. which is based on ECDH (elliptic-curve Diffie-Hellman), and mention some of the…
After the Anshel-Anshel-Goldfeld (AAG) key-exchange protocol was introduced in 1999, it was implemented and studied with braid groups and with the Thompson group as its underlying platforms. The length-based attack, introduced by Hughes and Tannenbaum, has been used to extensively study AAG with the braid group as the underlying platform. Meanwhile, a new platform, using polycyclic groups, was proposed by Eick and Kahrobaei. In this paper, we show that with a high enough Hirsch length, the polycyclic group as an underlying platform for AAG is resistant to the length-based attack. In particular…
Ring signature is a kind of group-oriented signature. It allows a member of a group to sign messages on behalf of the group without revealing his/her identity. Certificateless public key cryptography was first introduced by Al-Riyami and Paterson in Asiacrypt 2003. In certificateless cryptography, it does not require the use of certificates to guarantee the authenticity of users' public keys. Meanwhile, certificateless cryptography does not have the key escrow problem, which seems to be inherent in the Identity-based cryptography. In this paper, we propose a concrete certificateless ring signa…
Molecular communication in nanonetworks is an emerging communication paradigm that uses molecules as information carriers. Achieving a secure information exchange is one of the practical challenges that need to be considered to address the potential of molecular communications in nanonetworks. In this article, we have introduced secure channel into molecular communications to prevent eavesdropping. First, we propose a Diffie Hellman algorithm-based method by which communicating nanomachines can exchange a secret key through molecular signaling. Then, we use this secret key to perform ciphering…
The square root modulo problem is a known primitive in designing an asymmetric cryptosystem. It was first attempted by Rabin. Decryption failure of the Rabin cryptosystem caused by the 4-to-1 decryption output is overcome efficiently in this work. The proposed scheme (known as the AA_β- cryptosystem) has its encryption speed having a complexity order faster than the Diffie-Hellman Key Exchange, El-Gammal, RSA and ECC. It can also transmit a larger data set securely when compared to existing asymmetric schemes. It has a simple mathematical structure. Thus, it would have low computational requir…
Shor's shockingly fast quantum algorithm for solving the period-finding problem is a threat for the most common public-key primitives, as it can be efficiently applied to solve both the Integer Factorisation Problem and the Discrete Logarithm Problem. In other words, many once-secure protocols have to be replaced by still-secure alternatives. Instead of relying, for example, on the RSA protocol, the Diffie-Hellman key-exchange or the (Elliptic Curve) Digital Signature Algorithm, many researchers moved their attention to the design and analysis of primitives which are yet to be broken by quantu…
In a 2005 IACR report, Wang published an efficient identity-based key agreement protocol (IDAK) suitable for resource constrained devices. The author shows that the IDAK key agreement protocol is secure in the Bellare-Rogaway model with random oracles and also provides separate ad-hoc security proofs claiming that the IDAK protocol is not vulnerable to Key Compromise Impersonation attacks and also enjoys Perfect Forward Secrecy (PFS). In this report, we review the security properties of the protocol and point out that it is vulnerable to Unknown Key Share attacks. Although such attacks are oft…
We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement protocol. We analyze the computational difficulty of solving the mathematical problem underlying the proposed Abelian group law and we prove that the security of our proposal is equivalent to the discrete logarithm problem in the multiplicative group of the cubic extension of the finite field considered. Finally, we present a variant of the proposed group l…
The El-Gamal AA_β Public Key Cryptosystem is a new asymmetric cryptosystem based on the piecewise AA_β-function. The AA_β-function which is essentially a one way Boolean function was motivated by the squaring and multiplying process while computing g^a (mod p) in the Diffie Hellman key exchange procedure and also computing C \equiv M^e (mod N) and M \equiv C^d (mod N) in the RSA cryptosystem. It was also motivated by the add and double point operation E=kG in the elliptic curve cryptosystem. The hard mathematical problem surrounding this newly designed asymmetric cryptosystem is the NP-complet…
