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.
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…
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…
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…
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…
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）
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…
All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In this report we present computational evidence suggesting that an instance of the scheme called `MOBS' is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack.
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…
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…
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…
This paper introduces a novel entanglement-based QKD protocol, that makes use of a modified symmetric version of the Bernstein-Vazirani algorithm, in order to achieve a secure and efficient key distribution. Two variants of the protocol, one fully symmetric and one semi-symmetric, are presented. In both cases, the spatially separated Alice and Bob share multiple EPR pairs, one qubit of the pair each. The fully symmetric version allows both parties to input a secret key from the irrespective location and, finally, acquire in the end a totally new and original key, an idea which was inspired by …
Nowadays, Internet of Things (IoT) is a trending topic in the computing world. Notably, IoT devices have strict design requirements and are often referred to as constrained devices. Therefore, security techniques and primitives that are lightweight are more suitable for such devices, e.g., Static Random-Access Memory (SRAM) Physical Unclonable Functions (PUFs) and Elliptic Curve Cryptography (ECC). SRAM PUF is an intrinsic security primitive that is seeing widespread adoption in the IoT segment. ECC is a public-key algorithm technique that has been gaining popularity among constrained IoT devi…
Threshold schemes exist for many cryptographic primitives like signatures, key derivation functions, and ciphers. At the same time, practical key exchange protocols based on Diffie-Hellman (DH) or ECDSA primitives are not designed or implemented in a threshold setting. In this paper, we implement popular key exchange protocols in a threshold manner and show that this approach can be used in practice. First, we introduce two basic threshold DH key agreement schemes that provide enhanced security features in comparison with the classic DH primitive: dealerless distributed key generation, thresho…
Knowledge extraction, typically studied in the classical setting, is at the heart of several cryptographic protocols. We introduce the notion of secure quantum extraction protocols. A secure quantum extraction protocol for an NP relation $\mathcal{R}$ is a classical interactive protocol between a sender and a receiver, where the sender gets the instance $z$ and a witness $w$, while the receiver only gets the instance $z$. For any efficient quantum adversarial sender (who follows the protocol but can choose its own randomness), there exists a quantum extractor that can extract a witness $w'$ su…
