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Entropy

Non-Invertible Public Key Certificates

Luis Adrián Lizama-Pérez, J. Mauricio López R.

Published Feb 12, 2021• 7 citations
Publisher

Abstract

Post-quantum public cryptosystems introduced so far do not define a scalable public key infrastructure for the quantum era. We demonstrate here a public certification system based on Lizama's non-invertible key exchange protocol which can be used to implement a secure, scalable, interoperable and efficient public key infrastructure (PKI). We show functionality of certificates across different certification domains. Finally, we discuss a method that enables non-invertible certificates to exhibit perfect forward secrecy (PFS).

DOI
10.3390/e23020226

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Post-quantum public cryptosystems introduced so far do not define a scalable public key infrastructure for the quantum era. We demonstrate here a public certification system based on Lizama's non-invertible key exchange protocol which can be used to implement a secure, scalable, interoperable and efficient public key infrastructure (PKI). We show functionality of certificates across different certification domains. Finally, we discuss a method that enables non-invertible certificates to exhibit perfect forward secrecy (PFS).
We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in Fpn×n\mathbb{F}_p^{n \times n}Fpn×n​. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We show that the public, secret and channel keys become indistinguishable to the eavesdropper under matrix multiplication. Remarkably, for achieving a 512-bit security level, the public key is 1024 bits and the private key is 768 bits, making them the smallest keys among post-quantum key exchange algorithms. Also, we discuss how to achieve key authentication, interdomain certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.
As the quantum computing era approaches, securing classical cryptographic protocols becomes imperative. Public key cryptography is widely used for signature and key exchange but it’s the type of cryptography more threatened by quantum computing. Its application typically requires support via a public-key certificate, which is a signed data structure and must therefore face twice the quantum challenge: for the certified keys and for the signature itself. We present the latest developments in selecting robust Post-Quantum algorithms and investigate their applicability in the Public Key Infrastructure context. Our contribution entails defining requirements for a secure transition to a quantum-resistant Public Key Infrastructure, with a focus on adaptations for the X.509 certificate format. Additionally, we explore transitioning Certificate Revocation List and Online Certificate Status Protocol to support quantum-resistant algorithms. Through comparative analysis, we elucidate the complex transition to a quantum-resistant PKI.
The impending threat posed by quantum-capable adversaries necessitates a secure and practical transition of Public Key Infrastructures (PKIs) to support post-quantum cryptography (PQC). This paper addresses the multifaceted challenges of integrating PQC into existing PKI ecosystems by examining novel cryptographic combiners and hybrid certificate designs that can provide quantum-resistant security. We assess the performance, compatibility, and security of these hybrid certificates across standard communication protocols such as TLS, considering variations in root and intermediate certification paths. In addition, we introduce key management procedures that cover signature generation, validation, and lifecycle considerations under both software and hardware constraints. Beyond X.509, alternative trust models and certificate mechanisms are also analyzed for specialized domains, including IoT, firmware signing, and smart cards.
Development of Quantum Computers are growing rapidly, the security of today’s cryptographic systems which are working with Public Key Infrastructure (PKI) is at serious risk. RSA and ECC algorithms are the backbone of secure communication and digital identity can be breakable by quantum algorithms such as Shor’s. Hence, a transition is required to Post-Quantum Cryptography (PQC), which is designed to handle quantum attacks. This work provides a detailed review of how PQC can be integrated with the existing PKI, with a special focus on the auto-enrollment process. Auto-enrollment is an essential process but often overlooked mechanism, responsible for automatically issuing and renewing digital certificates. First, we explored how current PKI systems are exposed to the quantum threats and the readiness. The performance of the algorithms that are standardized by NIST, such as Kyber and Dilithium were discussed. We analyze the technical and operational challenges of transitioning to PQC by referencing both research studies and real-world implementations from major industry players such as Google and Microsoft. These include large key size, certificate size, compatibility issues, complex computations and need for crypto-agility. We also examine the hybrid approaches that combine classical and post-quantum methods as traditional strategies. The survey concludes by outlining best practices, deployment considerations, and open research challenges that must be addressed for a smooth, secure, and scalable shift to quantum-safe PKI. This work aims to guide researchers, engineers, and policymakers in building the next generation of cryptographic infrastructure that can stand the test-time even in a quantum world.
We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in Zpn×n\mathbb{Z}_p^{n \times n}Zpn×n​. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.
We introduce a new approach for circuit anonymous communication based on Lizama's non-invertible Key Exchange Protocol (ni-KEP) which has been conceived to work in the quantum era. Lizama's protocol has the smallest key size when compared to main post-quantum schemes thus it becomes a promising alternative for the quantum era. Circuit-based communication can be scaled to support the Hidden Service Protocol (HSP) as well as cross-domain digital certificates that promise greater computing security, speed and efficiency.