The Diffie–Hellman key exchange plays a crucial role in conventional cryptography, as it allows two legitimate users to establish a common, usually ephemeral, secret key. Its security relies on the discrete-logarithm problem, which is considered to be a mathematical one-way function, while the final key is formed by random independent actions of the two users. In the present work we investigate the extension of Diffie–Hellman key exchange to the quantum setting, where the two legitimate users exchange independent random quantum states. The proposed protocol relies on the bijective mapping of integers onto a set of symmetric coherent states, and we investigate the regime of parameters for which the map behaves as a quantum one-way function. Its security is analyzed in the framework of minimum-error-discrimination and photon-number-splitting attacks, while its performance and the challenges in a possible realization are also discussed.
The Diffie–Hellman key exchange plays a crucial role in conventional cryptography, as it allows two legitimate users to establish a common, usually ephemeral, secret key. Its security relies on the discrete-logarithm problem, which is considered to be a mathematical one-way function, while the final key is formed by random independent actions of the two users. In the present work we investigate the extension of Diffie–Hellman key exchange to the quantum setting, where the two legitimate users exchange independent random quantum states. The proposed protocol relies on the bijective mapping of integers onto a set of symmetric coherent states, and we investigate the regime of parameters for which the map behaves as a quantum one-way function. Its security is analyzed in the framework of minimum-error-discrimination and photon-number-splitting attacks, while its performance and the challenges in a possible realization are also discussed.
The Diffie-Hellman key exchange protocol introduced in 1976 allows two users, Alice and Bob, to establish a shared secret key K over insecure communication channels. With the rise of quantum computers, the protocol is in danger of becoming easily breakable. In response, several modified versions of Diffie-Hellman have been proposed claiming to be resistant to attacks performed by quantum computers. \n \nTwo such protocols and use of a semidirect product creating a modified version of a Discrete Logarithm problem to provide security for Alice and Bob. \n \nRegardless of choosing a tropical semiring or a free nilpotent p-group, these protocols prove not only vulnerable to quantum attacks, but they can be attacked by a classical computer. By exploiting each of the platforms, an eavesdropper Eve needs only to figure out how to mimic Alice's contribution to the shared secret key without needing to copy Alice's exact operations. By doing so, Eve can efficiently recover the shared secret key K.
This paper implements the concepts of perfect forward secrecy and the Diffie-Hellman key exchange using EPR pairs to establish and share a secret key between two non-authenticated parties and transfer messages between them without the risk of compromise. Current implementations of quantum cryptography are based on the BB84 protocol, which is susceptible to siphoning attacks on the multiple photons emitted by practical laser sources. This makes BB84-based quantum cryptography protocol unsuitable for network computing environments. Diffie-Hellman does not require the two parties to be mutually authenticated to each other, yet it can provide a basis for a number of authenticated protocols, most notably the concept of perfect forward secrecy. The work proposed in this paper provides a new direction in utilizing quantum EPR pairs in quantum key exchange. Although, classical cryptography boasts of efficient and robust protocols like the Diffie-Hellman key exchange, in the current times, with the advent of quantum computing they are very much vulnerable to eavesdropping and cryptanalytic attacks. Using quantum cryptographic principles, however, these classical encryption algorithms show more promise and a more robust and secure structure for applications. The unique properties of quantum EPR pairs also, on the other hand, go a long way in removing attacks like eavesdropping by their inherent nature of one particle of the pair losing its state if a measurement occurs on the other. The concept of perfect forward secrecy is revisited in this paper to attribute tighter security to the proposed protocol.
The Diffie–Hellman protocol, ingenious in its simplicity, is still the major solution in protocols for generating a shared secret in cryptography for e-trading and many other applications after an impressive number of decades. However, lately, the threat from a future quantum computer has prompted successors resilient to quantum computer-based attacks. Here, an algorithm similar to Diffie–Hellman is presented. In contrast to the classic Diffie–Hellman, it involves floating point numbers of arbitrary size in the generation of a shared secret. This can, in turn, be used for encrypted communication based on symmetric cyphers. The validity of the algorithm is verified by proving that a vital part of the algorithm satisfies a one-way property. The decimal part is deployed for the one-way function in a way that makes the protocol a post-quantum key generation procedure. This is concluded from the fact that there is, as of yet, no quantum computer algorithm reverse engineering the one-way function. An example illustrating the use of the protocol in combination with XOR encryption is given.
The necessity of a secure key exchange protocol arises from the critical need to establish encrypted communication over an untrusted network. Over time, a multitude of key exchange mechanisms have been developed to counteract adversarial threats. The Diffie-Hellman key exchange protocol (DHKE) is one of the most widely used protocols for symmetric key sharing. However, this protocol exhibits certain inherent limitations that attackers may exploit. It lacks authentication mechanism and is susceptible to Man-in-the-Middle (MITM) attacks and quantum attacks. To mitigate these vulnerabilities, we have designed a hybrid key exchange protocol combining DHKE with Learning With Errors (LWE), a lattice-based post-quantum primitive. This proposed protocol provides authentication via a Public Key Infrastructure (PKI) together with CRYSTALS-Dilithium digital signature, resilience against MITM attacks, and robustness against classical and quantum threats. We have done a security analysis using the Dolev-Yao threat model, extended to quantum-equipped attackers, and showed that the protocol achieves mutual authentication, session key secrecy, and forward secrecy under the hardness of LWE and DHKE. Lastly, we provided detailed parameter recommendations based on NIST standards and shed light on side-channel attacks.
In this paper, a quantum version of Diffie-Hellman key agreement protocol is developed using the commutative rotation transformations. Qubits rotated by secret rotation angles and exchanged over a quantum channel are appropriately measured to form a secret shared key. Additional 'slack' rotations are used to ensure that measurement of the commutative transformations always result in the same bit value, for legitimate party, in the absence of an eavesdropper. The performance of the quantum protocol is evaluated in terms of the number of exchanges needed for a given key size and the probability of detecting an eavesdropper. We also compare the proposed protocol with BB84.
Today's information society relies on cryptography to achieve security goals such as confidentiality, integrity, authentication, and non-repudiation for digital communications. Here, public-key cryptosystems play a pivotal role to share encryption keys and create digital signatures. However, quantum computers threaten the security of traditional public-key cryptosystems as they can tame computational problems underlying the schemes, i.e., discrete logarithm and integer factorization. The prospective arrival of capable-enough quantum computers already threatens today's secret communication in terms of their long-term secrecy when stored to be later decrypted. Therefore, researchers strive to develop and deploy alternative schemes.In this work, we evaluate a key exchange protocol based on combining public-key schemes with physical-layer security, anticipating the prospect of quantum attacks: If a powerful quantum attacker cannot immediately obtain a private key, legitimate parties have a window of short-term secrecy to perform a physical-layer jamming key exchange (JKE) to establish a long-term shared secret. Thereby, the protocol constraints the computation time available to the attacker to break the employed public-key cryptography. In this paper, we outline the protocol, discuss its security, and point out challenges to be resolved.