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arXiv:1903.03735

Post-Quantum Cryptographic Hardware Primitives

Lake Bu, Rashmi Agrawal, Cheng, Hai, Michel A. Kinsy

Published Mar 9, 2019• 1 citation
arXivHTMLPDF

Abstract

The development and implementation of post-quantum cryptosystems have become a pressing issue in the design of secure computing systems, as general quantum computers have become more feasible in the last two years. In this work, we introduce a set of hardware post-quantum cryptographic primitives (PCPs) consisting of four frequently used security components, i.e., public-key cryptosystem (PKC), key exchange (KEX), oblivious transfer (OT), and zero-knowledge proof (ZKP). In addition, we design a high speed polynomial multiplier to accelerate these primitives. These primitives will aid researchers and designers in constructing quantum-proof secure computing systems in the post-quantum era.

DOI
10.48550/arxiv.1903.03735

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The development and implementation of post-quantum cryptosystems have become a pressing issue in the design of secure computing systems, as general quantum computers have become more feasible in the last two years. In this work, we introduce a set of hardware post-quantum cryptographic primitives (PCPs) consisting of four frequently used security components, i.e., public-key cryptosystem (PKC), key exchange (KEX), oblivious transfer (OT), and zero-knowledge proof (ZKP). In addition, we design a high speed polynomial multiplier to accelerate these primitives. These primitives will aid researchers and designers in constructing quantum-proof secure computing systems in the post-quantum era.
The production of quantum computers with fast processing power and practical use will adversely affect the foundations of secure communication, especially for public-key cryptosystems (PKCs). Potential problems and solution scenarios are created early to design quantum-resistant PKCs. In this paper, the emergence of the concept of post-quantum cryptography (PQC) and early precautionary actions are explained. In addition, cryptosystem families that are known/believed to be secure in the presence of quantum computers are discussed. Based on these classes, the selected encryption/key encapsulation (KEM) and signature schemes of the NIST PQC process are expressed. Finally, some open problems for the post-quantum era are summarized.
The impending arrival of cryptographically relevant quantum computing threatens classical public‑key infrastructures. This paper reviews the latest developments (2025–2026) in post‑quantum cryptography (PQC), fully homomorphic encryption (FHE), and zero‑knowledge proofs (ZKP). NIST has advanced nine signature candidates to its third evaluation round and selected HQC as a backup encryption standard. Novel primitives include bio‑inspired RNA‑based cryptography, algebraic hash signatures, and topology‑mined lattice schemes. FHE has reached its fifth generation with the GL scheme and the MadPanthera virtual processor, while lightweight ZKPs such as Microsoft’s Vega enable mobile‑friendly verification. These advances demonstrate rapid maturation toward deployable quantum‑safe systems.
Quantum Computing threatens security of today’s systems. Confidence in today’s security technologies largely relies on Public Key Cryptography (PKC), which depends on computational difficulty of mathematical problems that cannot be solved efficiently using any technology available today. This will, however, change once a sufficiently capable quantum computer will become available. Similarly, security of symmetric crypto algorithms will also be substantially weakened. Current progress in research proves that Quantum Computing is no longer science fiction. Hence, research and development of post-quantum cryptographic algorithms that can withstand attacks in Quantum Computing era are of paramount importance. This paper complements existing research in this domain with a performance analysis of a post-quantum cryptosystem capable of encrypting and decrypting messages either bit-wise or string-wise. Specifically, we describe a workflow for implementing the scheme, design a reproducible hardware performance evaluation testbed for an IoT and an online shopping scenario, define performance metrics, and perform performance evaluation case studies. Our performance analysis shows that bit-wise encryption and decryption and the corresponding key generation fits resource-constrained IoT microcontrollers as well as on average laptops. The encryption and decryption of a bit each take less than 30 ms and the key generation less than 300 ms.
Lattice-based cryptography is one of the most promising candidates for designing post-quantum cryptographic algorithms that resist emerging quantum computing attacks. The recent NIST PQC standardization process is nearing its completion, with practical lattice-based algorithms for basic cryptographic functionalities (namely digital signature and public-key encryption) selected for standardization in the near future. However, practical lattice-based solutions for more advanced privacy-preserving protocols, in particular, Zero-Knowledge Proofs (ZKPs), have only emerged recently and are an active area of research. We discuss some recent developments in design and analysis of practical lattice-based post-quantum ZKPs and their applications. In particular, we review some challenges that arise in designing ZKPs in the lattice setting and some recent progress on efficient lattice-based Schnorr-like proofs for important relations, such as binary/range proofs, one-out-of-many proofs and rounding proofs [1, 2, 4]. We discuss applications and optimization of such proof systems as building blocks for practical advanced cryptographic protocols such as ring signatures and balance proofs for privacy-preserving cryptocurrency payment protocols [2, 3]. We also discuss our recent work on succinct designated-verifier ZKPs (DV-ZKSNARKS) for verifying correctness of general delegated computations [5].
The security of current public-key cryptosystems relies on the hardness of factoring large integers or solving discrete logarithm problems. However, these mathematical problems can be solved in polynomial time using a quantum computer. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. In this expository article, we give an overview of recent research on post-quantum cryptography. In particular, we describe the construction and security of multivariate polynomial cryptosystems and lattice-based cryptosystems, which are the main candidates of post-quantum cryptography.
Basic security requirements such as confidentiality, user authentication and data integrity, are assured by using public-key cryptography (PKC). In particular, public-key signature schemes provide non-repudiation, integrity of transmitted messages and authentication. The presence of a large scale quantum computer would be a real threat to break the most widely used public-key cryptographic algorithms in practice, RSA, DSA, ECDSA signature schemes and Diffie-Hellman key exchange. Thus, all security protocols and applications where these public-key cryptographic algorithms are used are vulnerable to quantum-computer attacks. There are five directions of cryptographic primitives secure against a quantum computer: multivariate quadratic equation-based, hash-based, lattice-based, code-based and supersingular isogeny-based cryptography. These primitives could serve as replacements for current public-key cryptographic algorithms to prepare for post-quantum era. It is important to prioritize the fields to be replaced by post-quantum cryptography (PQC) since it is hard to replace the currently deployed PKC with PQC at the same time. The fields directly connected to human life such as vehicular communications should be the primary targets of PQC applications. This survey is dedicated to providing guidelines for adapting the most suitable post-quantum candidates to the requirements of various devices and suggesting efficient and physically secure implementations that can be built into existing embedded applications as easily as traditional PKC. It focuses on the five types of post-quantum signature schemes and investigates their theoretical backgrounds, structures, state-of-the-art constructions and implementation aspects on various platforms raging from resource constrained IoT devices to powerful servers connected to the devices for secure communications in post-quantum era. It offers appropriate solutions to find tradeoffs between key sizes, signature lengths, performance, and security for practical applications.