Page 229 - Cyber Defense eMagazine September 2025

Technical Threats: Shor’s and Grover’s Algorithms

The threat is best understood through two quantum algorithms—Shor’s and Grover’s, which can be
seen as the “unlocking formulas” of the quantum era.

Shor’s Algorithm (1994) revolutionized theoretical cryptanalysis by demonstrating that a sufficiently
powerful quantum machine could factor large integers and solve discrete logarithms exponentially faster
than classical methods. This is devastating news for RSA and ECC encryption, which rely on these
mathematical problems being computationally infeasible (NIST, 2023).

As an example, RSA-2048, considered secure because factoring such large numbers would take billions
of years for classical hardware—could theoretically be broken in minutes with a large enough quantum
computer. The implications for banking, e-commerce, and secure government communications are
staggering.

Grover’s Algorithm, while not as directly destructive to public-key crypto, still poses a significant threat.
It offers a quadratic speed-up for brute-force searches, effectively halving the security level of symmetric-
key algorithms and hash functions like SHA-2 and SHA-3 (NSA, 2022). This means that to maintain
equivalent security, organizations will need to double their key sizes.

Algorithm Target Quantum Advantage Security Impact

Shor’s RSA & ECC encryption Exponential factoring Breaks RSA-2048/ECC-256
Algorithm speed-up in hours

Grover’s Hash functions (SHA-2, Quadratic brute-force Reduces effective bit
Algorithm SHA-3) acceleration strength by ~50%

The Real and Hypothetical Impact

The quantum threat extends across multiple domains:

Finance: Online banking, stock exchanges, and payment processors rely heavily on RSA and ECC. A
quantum-enabled breach could allow not just theft but digital fabrication of valid transactions—
undermining trust in the financial system.

Government and Defense: Public Key Infrastructure (PKI) secures sensitive inter-agency
communication. Under the harvest-now, decrypt-later threat model, adversaries can store encrypted
communications today with the intention of decrypting them once powerful quantum technology is
available (NSA, 2022).

Cyber Defense eMagazine – September 2025 Edition 229
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