The NISQ Complexity of Collision Finding: Implications for Quantum Algorithms in the Noisy-Intermediate Scale Quantum Era

Core Concepts

The author explores the impact of quantum computing on collision finding complexity, highlighting the need for longer hash outputs due to quantum adversaries. The study introduces models for NISQ algorithms and provides tight bounds for each.

Abstract

The content delves into collision-resistant hashing's importance in cryptography, detailing classical and quantum complexities. It discusses implications of quantum attacks in the NISQ era, introducing models and proving lower bounds for collision finding and preimage search.

Stats

Θ(N 1/2) queries needed to find a collision classically.
Full-scale quantum adversaries require Θ(N 1/3) queries to find a collision.
Output length adjustment to 384 bits needed for security against quantum algorithms running in time 2^128.
Lower bounds established for NISQ preimage search and collision finding.
Optimal success probability analysis for hybrid algorithms making adaptive quantum or classical queries with limited budgets.
Noise affects noisy oracle queries with dephasing noise b ∈ [1/t, 1].
Bounded Quantum Depth model optimal success probability is Θ(dt^2/N).

Quotes

"The emergence of quantum computing requires us to significantly reevaluate existing cryptography since quantum adversaries can be much more powerful."
"Should we sacrifice efficiency for potential quantum attacks, especially in the NISQ era?"
"Our results handle all regimes between NISQ and full-scale quantum computers."

Key Insights Distilled From

The NISQ Complexity of Collision Finding

by Yassine Hamo... at arxiv.org 02-29-2024

https://arxiv.org/pdf/2211.12954.pdf

Deeper Inquiries

How can the findings on collision resistance impact future cryptographic protocols

The findings on collision resistance have significant implications for future cryptographic protocols. Collision-resistant hashing is a fundamental primitive in modern cryptography, forming the basis of various cryptographic applications such as digital signatures, Merkle trees, and zero-knowledge proofs. Understanding the complexity of collision resistance is crucial for ensuring the security of these applications.
With advancements in quantum computing and the ability of quantum adversaries to find collisions more efficiently, it becomes imperative to enhance collision resistance in cryptographic protocols. The results on collision finding provide insights into the level of security required against quantum attacks. Future cryptographic protocols may need to adapt by increasing hash output lengths or implementing stronger collision-resistant algorithms to withstand potential threats from quantum adversaries.
In essence, the findings on collision resistance can drive innovation in developing more robust and secure cryptographic protocols that are resilient against emerging threats posed by quantum computing.

What are potential drawbacks of sacrificing efficiency for security against quantum attacks

While prioritizing security against quantum attacks is essential in cryptography, sacrificing efficiency for this purpose can have certain drawbacks. One potential drawback is related to performance and computational resources. Increasing key lengths or using longer hash outputs for enhanced security can lead to increased computational overhead and slower processing speeds. This could impact system performance and responsiveness, especially in real-time applications where speed is critical.
Moreover, sacrificing efficiency for security might also result in higher resource utilization and energy consumption. In scenarios where resources are limited or energy efficiency is a concern (e.g., IoT devices), trading off efficiency for heightened security measures could pose challenges.
Additionally, focusing solely on enhancing security without considering efficiency aspects may lead to complex implementations that are difficult to manage or maintain over time. Striking a balance between security requirements and operational efficiency is crucial to ensure that cryptographic protocols remain effective while minimizing any negative impacts on performance.

How might advancements in NISQ algorithms influence broader applications beyond cryptography

Advancements in NISQ (Noisy-Intermediate Scale Quantum) algorithms have the potential to influence broader applications beyond cryptography by unlocking new capabilities and enabling innovative solutions across various domains:

Optimization Problems: NISQ algorithms can be leveraged for solving optimization problems efficiently through techniques like variational algorithms or hybrid classical-quantum approaches. This has implications for industries such as logistics, finance, drug discovery, and supply chain management where optimization plays a vital role.

Machine Learning: NISQ algorithms offer opportunities for accelerating machine learning tasks such as pattern recognition, clustering analysis, feature selection, etc., leading to advancements in AI models' training processes with improved speed and accuracy.

Quantum Simulation: NISQ computers enable researchers to simulate complex physical systems accurately at scales beyond classical computation's reach—impacting fields like material science research or climate modeling with profound insights into natural phenomena.

4 .Secure Communication: Quantum technologies based on NISQ principles hold promise for developing ultra-secure communication networks resistant against eavesdropping due their inherent properties like entanglement-based encryption methods
Overall ,the progress made towards practical implementation will open up new avenues across diverse sectors revolutionizing how we approach complex problems through advanced computational paradigms offered by NISQ era technology .