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 where there is no group law. We include details on four implementations of qDSA, using Montgomery and fast Kummer surface arithmetic on the 8-bit AVR ATmega and 32-bit ARM Cortex M0 platforms. We find that qDSA significantly outperforms state-of-the-art signature implementations in terms of stack usage and code size. We also include an efficient compression algorithm for points on fast Kummer surfaces, reducing them to the same size as compressed elliptic curve points for the same security level.
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…
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…
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…
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…
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…
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 …
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 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 prese…
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）
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.
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…
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…
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…
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…
This work is based on the proposal of a deterministic randomness extractor of a random Diffie-Hellman element defined over two prime order multiplicative subgroups of a finite fields $\mathbb{F}_{p^n}$, $G_1$ and $G_2$. We show that the least significant bits of a random element in $G_1*G_2$, are indistinguishable from a uniform bit-string of the same length. One of the main application of this extractor is to replace the use of hash functions in pairing by the use of a good deterministic randomness extractor.
The paper reviews an implementation of an additional encrypted tunnel within TLS to further secure and authenticate the traffic of personal information between ProtonMail's frontends and the backend, implementing its key exchange, symmetric packet encryption, and validation. Technologies such as Secure Remote Password (SRP) and the Elliptic Curves Diffie Hellman Ephemeral (ECDHE) exchange are used for the key exchange, verifying the public parameters through PGP signatures. The data is then transferred encrypted with AES-128-GCM. This project is meant to integrate TLS security for high securit…
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.
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.
The rapid development of computer technology will be the whole world as a whole, the widespread application of instant messaging technology to bring great convenience to people's lives, while privacy protection has become a more significant problem. For ordinary it's hard to equip themselves with a cryptograph machine. In this paper, through in-depth study of elliptic curve cryptosystem ECC and advanced encryption standard AES encryption algorithm, according to the characteristics of public key cryptography, elliptic curve version through the establishment of Diffie-Hellman key exchange protoc…
We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits, we propose a key exchange protocol given in a matrix form, with four independent entries each of them constructed with 64 bits. Apart from the great advantage of significantly reducing the number of used bits, this methodology appears to be immune to attacks of the style of Western, Miller, and Adleman, and at the same time it is also able to reach the same …
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…
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…
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…
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…
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…
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…
With the rapid growth of smartphone and tablet users, Device-to-Device (D2D) communications have become an attractive solution for enhancing the performance of traditional cellular networks. However, relevant security issues involved in D2D communications have not been addressed yet. In this paper, we investigate the security requirements and challenges for D2D communications, and present a secure and efficient key agreement protocol, which enables two mobile devices to establish a shared secret key for D2D communications without prior knowledge. Our approach is based on the Diffie-Hellman key…
