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Post-quantum alternative to secure sockets

Marek Behún

Published Jan 31, 2017• 0 citations
OpenAlex

Abstract

The goal of this thesis is to implement a software library that provides a wrapping of real-time socket- like communication into an cryptographic protocol with purpose similar to SSL or TLS, that is secure against an adversary in possession of a quantum computer. Resulting software utilizes the Supersingular Isogeny Diffie Hellman (SIDH) key-exchange algorithm for achieving this level of security, and is simple, portable and independent on system-specific primitives. The thesis gives a concise introduction to the theory on which SIDH is built, targeting the audience of undergraduate students of Computer Science. Powered by TCPDF (www.tcpdf.org)

Related papers

Isogeny-based post-quantum key exchange protocols

Ernest Sorinas Capdevila

The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented.

•Jan 1, 2020•0 citations

Advancements in Isogeny-Based Cryptography: A Mathematical Approach to Post-Quantum Security

Abhay Soni, Sunidhi Singh, Atul Chaturvedi

In this paper, we have discussed isogeny-based cryptography as a rather appealing option for post-quantum security. We provide analysis of current protocols like SIDH (Supersingular Isogeny Diffie-Hellman) and SIKE (Supersingular Isogeny Key Encapsulation) setting up fundamental issues with their security and performance. In this work we introduce a novel isogeny pathfinding algorithm that employs graph theory as well as probabilistic models in order to lower its computational complexity. The results show significant improvement in both efficiency and security, strengthening the case for the use of isogeny based systems in a quantum-resilient cryptographic space.

IEEE International Students' Conference on Electrical, Electronics and Computer Science (SCEECS)•Jan 18, 2025•2 citations

Isogeny-Based Post-Quantum Cryptography

Ashneet Khandpur Singh

The present thesis focus on one of the post-quantum cryptosystems, in particular, the isogenybased cryptography. Because of its certain properties like the hard problem of computing isogenies between two elliptic curves, it makes it to be one of the few candidates for post-quantum cryptography. We will study the algorithms based on this isogeny-based cryptography and why they are useful against quantum computers. One of these algorithms is the Supersingular Isogeny Diffie Hellman (SIDH), a candidate for substituing ECDH in the Signal protocol to make it quantum safe.

•Oct 1, 2019•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

Elliptic Curve Isogenies: A New Frontier for Post-Quantum Cryptography

PAULO SÉRGIO DE ANDRADE

The rise of quantum computing poses a significant threat to contemporary public-key cryptography, which relies on problems like integer factorization and the discrete logarithm, both of which are solvable in polynomial time by Shor's algorithm. This has prompted a global effort to develop and standardize post-quantum cryptographic primitives that are resistant to attacks by both classical and quantum computers. Among the various families of post-quantum candidates, isogeny-based cryptography has emerged as a particularly compelling, albeit challenging, alternative. This paper explores the mathematical foundations of elliptic curve isogenies and their application as a basis for quantum-resistant cryptographic protocols. We delve into the structure of supersingular elliptic curves and the associated isogeny graphs, which form the basis for the conjectured hardness of the underlying computational problems. The Supersingular Isogeny Diffie-Hellman (SIDH) protocol and its derivative, Supersingular Isogeny Key Encapsulation (SIKE), are examined in detail as principal examples of this cryptographic paradigm. We analyze their key advantages, most notably their exceptionally small key sizes, which offer significant benefits for constrained environments. However, the security landscape of isogeny-based cryptography has been dramatically reshaped by recent cryptanalytic breakthroughs that completely broke the SIKE protocol. This paper analyzes the nature of these attacks, discussing the vulnerabilities they exploited and the profound implications for the field. We conclude by surveying the current state of isogeny-based cryptography in the aftermath of these developments, outlining the proposed countermeasures, alternative designs, and the open research questions that define the new frontier for this promising area of post-quantum cryptography.

•Nov 14, 2025•0 citations

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
The goal of this thesis is to implement a software library that provides a wrapping of real-time socket- like communication into an cryptographic protocol with purpose similar to SSL or TLS, that is secure against an adversary in possession of a quantum computer. Resulting software utilizes the Supersingular Isogeny Diffie Hellman (SIDH) key-exchange algorithm for achieving this level of security, and is simple, portable and independent on system-specific primitives. The thesis gives a concise introduction to the theory on which SIDH is built, targeting the audience of undergraduate students of Computer Science. Powered by TCPDF (www.tcpdf.org)
The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented.
In this paper, we have discussed isogeny-based cryptography as a rather appealing option for post-quantum security. We provide analysis of current protocols like SIDH (Supersingular Isogeny Diffie-Hellman) and SIKE (Supersingular Isogeny Key Encapsulation) setting up fundamental issues with their security and performance. In this work we introduce a novel isogeny pathfinding algorithm that employs graph theory as well as probabilistic models in order to lower its computational complexity. The results show significant improvement in both efficiency and security, strengthening the case for the use of isogeny based systems in a quantum-resilient cryptographic space.
The present thesis focus on one of the post-quantum cryptosystems, in particular, the isogenybased cryptography. Because of its certain properties like the hard problem of computing isogenies between two elliptic curves, it makes it to be one of the few candidates for post-quantum cryptography. We will study the algorithms based on this isogeny-based cryptography and why they are useful against quantum computers. One of these algorithms is the Supersingular Isogeny Diffie Hellman (SIDH), a candidate for substituing ECDH in the Signal protocol to make it quantum safe.
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 rise of quantum computing poses a significant threat to contemporary public-key cryptography, which relies on problems like integer factorization and the discrete logarithm, both of which are solvable in polynomial time by Shor's algorithm. This has prompted a global effort to develop and standardize post-quantum cryptographic primitives that are resistant to attacks by both classical and quantum computers. Among the various families of post-quantum candidates, isogeny-based cryptography has emerged as a particularly compelling, albeit challenging, alternative. This paper explores the mathematical foundations of elliptic curve isogenies and their application as a basis for quantum-resistant cryptographic protocols. We delve into the structure of supersingular elliptic curves and the associated isogeny graphs, which form the basis for the conjectured hardness of the underlying computational problems. The Supersingular Isogeny Diffie-Hellman (SIDH) protocol and its derivative, Supersingular Isogeny Key Encapsulation (SIKE), are examined in detail as principal examples of this cryptographic paradigm. We analyze their key advantages, most notably their exceptionally small key sizes, which offer significant benefits for constrained environments. However, the security landscape of isogeny-based cryptography has been dramatically reshaped by recent cryptanalytic breakthroughs that completely broke the SIKE protocol. This paper analyzes the nature of these attacks, discussing the vulnerabilities they exploited and the profound implications for the field. We conclude by surveying the current state of isogeny-based cryptography in the aftermath of these developments, outlining the proposed countermeasures, alternative designs, and the open research questions that define the new frontier for this promising area of post-quantum cryptography.
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.