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arXiv:2103.00598

Non-invertible Anonymous Communication for the Quantum Era

Luis Adrián Lizama-Pérez

Published Feb 28, 2021• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2103.00598

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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.
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.
We introduce a novel key exchange protocol based on non-commutative matrix multiplication. 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 opportunity for the eavesdropper to get the private key is by means of an exhaustive search which is equivalent to searching an unsorted database problem. Therefore, the algorithm becomes a promising candidate to be used in the quantum era to establish shared keys and achieve secret communication. Furthermore, to establish a 256-bit secret key the size of the public key only requires 256 bits while the private key occupies just 384 bits. Matrix multiplications can be done over a reduced 4-bit size modulo. Also, we show that in a generalized method, private numbers become indistinguishable and we discuss how to achieve Perfect Forward Secrecy (PFS). As a consequence, Lizama's protocol becomes a promising alternative for Internet-of-Things (IoT) computational devices in the quantum era.
As we move further into the era of digital transformation, cloud services are becoming a cornerstone across industries such as healthcare, agriculture, and Industry 4.0. These sectors increasingly rely on cloud environments to collect, process, and store vast amounts of data, often integrated with smart devices. While ensuring high availability and efficiency remains vital, the paramount concern is maintaining data security. This challenge becomes even more pressing in a world where quantum computers pose a serious threat to traditional cryptographic methods. Classical encryption schemes, particularly those relying on computational hardness assumptions, are susceptible to quantum attacks. This paper proposes a solution by combining the theoretically unbreakable One-Time Pad (OTP) encryption with quantum-safe key exchange protocols. Through the integration of Quantum Key Distribution (QKD) and post-quantum cryptographic techniques, we outline a robust framework designed to secure communication in the coming quantum era.
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.
The emergence of quantum computing poses a threat to classical cryptography algorithms, necessitating a shift to quantum secure cryptography. Hybrid protocols combining at least one classical and one quantum-resistant cryptographic algorithm are becoming the standard for securing communications. In this work, we present our novel solution for integrating three different cryptographic assumptions (two of them quantumresistant) into hybrid network security protocols, ensuring that three different cryptographic assumptions must be broken before the protocol becomes vulnerable. Our solution allows for a seamless integration of classical and post-quantum (PQ) cryptography, and quantum key distribution (QKD) into existing network security protocols (e.g., TLS, IPsec) without any major modifications to the protocols themselves. This crypto-agility ensures the mitigation of some of the most well known challenges of both PQ cryptography and QKD. Our findings demonstrate the feasibility of such triple-hybrid network security protocols, showing non-substantial decrease in performance and almost no added packet overhead compared to state of the art protocols. In exchange, we pave the way towards next generation networks where the potential of new quantum-resistant cryptographic schemes can be leveraged in a dynamic and agile fashion, thus fostering a new era of unbreakable communication systems.