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Apress eBooks

Faster Search plus Threatening the Foundation of Asymmetric Cryptography with Grover and Shor

Vladimir Silva

Published Jan 1, 2018• 0 citations
Publisher

Abstract

This chapter brings proceedings to a close with two algorithms that have generated excitement about the possibilities of practical quantum computation:
DOI
10.1007/978-1-4842-4218-6_8

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For decades, classical computers have been governed by predictable rules. But as we approach the physical limits of computation, a new paradigm is emerging. Quantum computing operates on the strange and powerful laws of quantum mechanics—superposition, entanglement, and interference—to tackle problems far beyond the reach of any classical machine. The true potential of this field was unlocked by two landmark discoveries: Shor’s algorithm, a revolutionary method for integer factorization that threatens to upend modern cryptography, and Grover’s algorithm, a versatile tool that offers a quadratic speedup for unstructured search problems. This paper serves as a guide to these foundational algorithms, detailing their inner workings and their profound impact. We also explore post-quantum cryptography, hybrid frameworks, and quantum machine learning—illustrating the evolving role of quantum algorithms in shaping the future of science and technology.
This chapter explains the evolution and future risks to cryptography from quantum computing. It outlines key historical developments from ancient ciphers through World War II (WWII) innovations like Enigma and Colossus, to modern symmetric and asymmetric encryption systems. It highlights RSA, Diffie-Hellman, and AES, and introduces digital certificates and HTTPS protocols. The chapter then shifts to the quantum threat, explaining how Shor's algorithm breaks asymmetric encryption and Grover's weakens symmetric methods. It details the “harvest now, decrypt later” risk, emphasizing the urgency of post-quantum cryptography. NIST's efforts to standardize quantum-resistant algorithms are noted. The chapter concludes with a breakdown of symmetric, asymmetric, and hash-based cryptographic methods, their applications, and quantum-era challenges. The focus is on the need for proactive migration strategies and resilient cryptographic frameworks before quantum systems become practically deployable, potentially by 2030. The chapter serves as a foundational guide for understanding and responding to the quantum disruption of cryptographic security.