Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Cryptography

An Alternative Diffie-Hellman Protocol

Eric Järpe

Published Feb 25, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.3390/cryptography4010005

Related papers

Secure Messaging Using Post-Quantum Key Sharing Based on CSIDH and Fujisaki-Okamoto Transform

Rakotondramanana Radiarisainana Sitraka, Ramafiarisona Hajasoa Malalatiana, Randrianandrasana Marie Emile +1 more

Preserving the confidentiality of information exchanges relies fundamentally on an end-to-end encryption system, involving the use of a secret key to secure the entire communication. However, with the imminent emergence of quantum computing, threats to traditional encryption systems are multiplying. This is where post-quantum key sharing, in particular the Commutative Super Isogenies Diffie Hellman (CSIDH) algorithm, comes in. The CSIDH uses the ideal of some class number to a morphism of elliptic curve for calculating the shared key. It offers an innovative solution for secure key generation between two users, while providing a robust defense against potential attacks from quantum computers, whose computing power is redefining the limits of cryptographic security, based on the mathematical foundations of elliptic curves and isogeny. This technological advance represents an essential pillar in preserving the confidentiality of communications, in a context where security challenges are constantly evolving. Combining with Fujisaki-Okamoto transform, socket, and Linux; a chat application over python could be created for transmitting secure messages.

International Journal of Scientific Research in Computer Science Engineering and Information Technology•Mar 25, 2024•0 citations

Vulnerabilities of some semidirect products in Diffie-Hellman key exchanges

Dylan Rudy

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.

•May 1, 2021•0 citations

Post-Quantum Security of Communication and Messaging Protocols: Achievements, Challenges and New Perspectives

Julia Bobrysheva, Sergey Vladimirovich Zapechnikov

Widely used communication and messaging protocols, e.g., TLS 1.3 and Signal, are insecure against an adversary with a quantum computer. We expect that post-quantum security will become mandatory for a new generation of cryptographic protocols in the nearest 10-15 years. The analysis of existing post-quantum secure cryptographic tools for key exchange, encryption and message authentication based on hard problems in codes, lattices, ring learning with errors and elliptic curve isogenies revealed their advantages and drawbacks. In particular, we conclude, that the main threat to communication and messaging protocols is only pre-quantum security of currently used Diffie-Hellman key exchange protocols. We summarize efficiency and safety results for each class of post-quantum cryptographic schemes and present an experimental implementation of isogeny-based Diffie-Hellman-like key exchange protocol as an illustration of their applicability.

IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering•Jan 1, 2019•4 citations

Quantum Diffie–Hellman key exchange

Georgios M. Nikolopoulos

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.

arXiv:2501.09568•APL Quantum•Jan 16, 2025•1 citation

Quantum-Safe Cryptography

Kunal Meher

The defense of public key cryptography (PKC) lies in computational issues like the difficulty of factorizing enormous prime numbers and the discrete logarithm calculations. Such kinds of algorithms are called one-way functions because although it is straightforward to compute output given input, it is difficult to compute input if output is given. It is expected that such numerical or computational issues which are utilized in current cryptographic plans are difficult to address for an adversary utilizing present PCs. Yet, many organizations are attempting to assemble a high-powered quantum PC and in the future quantum PCs will be available for business use. Traditional asymmetric cryptographic algorithms are not secure against strong quantum machines. Shor’s algorithm running on a powerful quantum PC is able to solve integer factorization problems and discrete logarithm problems in polynomial time. So, asymmetric algorithms that are used today, like RSA, DSA and Diffie-Hellman will become insecure. Similarly, Grover’s algorithm running on a powerful quantum computer poses a serious threat to symmetric key algorithms which uses small key size. There is a need to work on alternate algorithms to resist quantum threat. NIST has already started with a process for the standardization of algorithms which are known as post-quantum cryptography (PQC) algorithms. Specialists globally are exploring progress toward post-quantum cryptography.

Chapman & Hall/CRC eBooks•Aug 9, 2023•3 citations

Post-Quantum Cryptography for Secure Communication: A Systematic Review of Algorithms, Performance Trade-offs, and Emerging Challenges

Suvhodip Saha

The rapid growth of quantum computing poses a critical threat to classical cryptographic systems. That is due in large part to the fact that they represent efficient solutions for some of the most challenging mathematical problems such as integer factoring or finding discrete logarithms. Schemes currently in wide use including RSA, Diffie–Hellman, and elliptic curve cryptography are particularly susceptible to being attacked by quantum computers, using algorithms like Shor's Algorithm and Grover's Algorithm. The advent of post-quantum cryptography (PQC) provides a promising potential answer to providing longterm security from adversaries using quantum computing capabilities. This paper presents a comprehensive state-of-the-art review of various PQC techniques currently being researched, including lattice-based methods, code-based methods, multivariate methods, hash-based methods, and isogeny-based methods. key challenges that will need to be addressed include computational overhead, large key sizes and implementation complexity. Furthermore the study reviews the current standardization efforts by the National Institute of Standards and Technology related to PQC and discusses some of the very specific practical considerations that need to be considered before widely deploying these techniques. The paper concludes by a complete list of existing research challenges and proposed future work that will assist in the development of efficient and scalable systems that will resist attacks from quantum computers.

International Journal for Research in Applied Science and Engineering Technology•Mar 24, 2026•0 citations
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.
Preserving the confidentiality of information exchanges relies fundamentally on an end-to-end encryption system, involving the use of a secret key to secure the entire communication. However, with the imminent emergence of quantum computing, threats to traditional encryption systems are multiplying. This is where post-quantum key sharing, in particular the Commutative Super Isogenies Diffie Hellman (CSIDH) algorithm, comes in. The CSIDH uses the ideal of some class number to a morphism of elliptic curve for calculating the shared key. It offers an innovative solution for secure key generation between two users, while providing a robust defense against potential attacks from quantum computers, whose computing power is redefining the limits of cryptographic security, based on the mathematical foundations of elliptic curves and isogeny. This technological advance represents an essential pillar in preserving the confidentiality of communications, in a context where security challenges are constantly evolving. Combining with Fujisaki-Okamoto transform, socket, and Linux; a chat application over python could be created for transmitting secure messages.
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.
Widely used communication and messaging protocols, e.g., TLS 1.3 and Signal, are insecure against an adversary with a quantum computer. We expect that post-quantum security will become mandatory for a new generation of cryptographic protocols in the nearest 10-15 years. The analysis of existing post-quantum secure cryptographic tools for key exchange, encryption and message authentication based on hard problems in codes, lattices, ring learning with errors and elliptic curve isogenies revealed their advantages and drawbacks. In particular, we conclude, that the main threat to communication and messaging protocols is only pre-quantum security of currently used Diffie-Hellman key exchange protocols. We summarize efficiency and safety results for each class of post-quantum cryptographic schemes and present an experimental implementation of isogeny-based Diffie-Hellman-like key exchange protocol as an illustration of their applicability.
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 defense of public key cryptography (PKC) lies in computational issues like the difficulty of factorizing enormous prime numbers and the discrete logarithm calculations. Such kinds of algorithms are called one-way functions because although it is straightforward to compute output given input, it is difficult to compute input if output is given. It is expected that such numerical or computational issues which are utilized in current cryptographic plans are difficult to address for an adversary utilizing present PCs. Yet, many organizations are attempting to assemble a high-powered quantum PC and in the future quantum PCs will be available for business use. Traditional asymmetric cryptographic algorithms are not secure against strong quantum machines. Shor’s algorithm running on a powerful quantum PC is able to solve integer factorization problems and discrete logarithm problems in polynomial time. So, asymmetric algorithms that are used today, like RSA, DSA and Diffie-Hellman will become insecure. Similarly, Grover’s algorithm running on a powerful quantum computer poses a serious threat to symmetric key algorithms which uses small key size. There is a need to work on alternate algorithms to resist quantum threat. NIST has already started with a process for the standardization of algorithms which are known as post-quantum cryptography (PQC) algorithms. Specialists globally are exploring progress toward post-quantum cryptography.
The rapid growth of quantum computing poses a critical threat to classical cryptographic systems. That is due in large part to the fact that they represent efficient solutions for some of the most challenging mathematical problems such as integer factoring or finding discrete logarithms. Schemes currently in wide use including RSA, Diffie–Hellman, and elliptic curve cryptography are particularly susceptible to being attacked by quantum computers, using algorithms like Shor's Algorithm and Grover's Algorithm. The advent of post-quantum cryptography (PQC) provides a promising potential answer to providing longterm security from adversaries using quantum computing capabilities. This paper presents a comprehensive state-of-the-art review of various PQC techniques currently being researched, including lattice-based methods, code-based methods, multivariate methods, hash-based methods, and isogeny-based methods. key challenges that will need to be addressed include computational overhead, large key sizes and implementation complexity. Furthermore the study reviews the current standardization efforts by the National Institute of Standards and Technology related to PQC and discusses some of the very specific practical considerations that need to be considered before widely deploying these techniques. The paper concludes by a complete list of existing research challenges and proposed future work that will assist in the development of efficient and scalable systems that will resist attacks from quantum computers.