Compute Resource Expenditures Over the Next 100 Years and Bypass Probabilities at 1, 5, 10, 50, and 100 Years
Table of Contents
- Introduction
- Exponential Compute Growth Model
- Compute Resource Expenditures Over 100 Years
- Bypass Probabilities at Each Time Interval
- Implications for VoiceKey Security
- Conclusion
- References
- Contact Information
- Acknowledgments
Introduction
Understanding the future landscape of computational resources is crucial for assessing the long-term security of authentication systems like VoiceKey. This document analyzes compute resource expenditures over the next 100 years, assuming exponential growth, and evaluates the probabilities of bypassing the VoiceKey system at specific intervals: 1 year, 5 years, 10 years, 50 years, and 100 years.
By representing data logarithmically, we simplify the visualization of exponential growth and its impact on security over time.
Exponential Compute Growth Model
Historical Trends in Compute Growth
- Moore’s Law: Historically, the number of transistors on integrated circuits has doubled approximately every 18 to 24 months.
- Compute Performance: Computational power has increased exponentially, leading to significant advancements in processing capabilities.
- Limitations: Physical and economic factors may eventually limit this growth, but new technologies (e.g., quantum computing) could sustain or accelerate it.
Logarithmic Representation for Simplicity
- Logarithmic Scale: Allows us to represent exponential growth as a linear trend, simplifying analysis and visualization.
- Impact: Makes it easier to compare orders of magnitude over long time periods.
Compute Resource Expenditures Over 100 Years
Compute Growth Projections
Assuming a consistent exponential growth rate, we can model compute resources over the next 100 years.
Assumptions
Logarithmic Representation
-
By taking the logarithm (base 10) of the compute capacities, we simplify the values:
[
\log_{10}(C(t)) = \log_{10}(C_0) + \left( \frac{t}{T_d} \times \log_{10}(2) \right)
]
-
Compute the logarithmic values at each time point.
Logarithmic Visualization
| Time (Years) |
Compute Capacity (( C(t) )) |
( \log_{10}(C(t)) ) |
| 0 |
( 1 \times 10^{18} ) FLOPS |
18 |
| 1 |
( 1.587 \times 10^{18} ) |
18.20 |
| 5 |
( 1 \times 10^{19} ) |
19 |
| 10 |
( 1 \times 10^{20} ) |
20 |
| 50 |
( 1.07 \times 10^{28} ) |
28.03 |
| 100 |
( 1.15 \times 10^{38} ) |
38.06 |
- The logarithmic scale shows a linear increase, simplifying comparisons over time.
Bypass Probabilities at Each Time Interval
Methodology for Estimating Bypass Probabilities
- Attacker’s Compute Resources: Assume that attackers can access up to a certain percentage of global compute capacity.
- Bypass Difficulty: The difficulty to bypass VoiceKey increases exponentially due to the reliance on hard-to-replicate features.
- Compute Exhaustion Principle: The system aims to require more compute resources to bypass than is feasibly available to an attacker.
Analysis at 1, 5, 10, 50, and 100 Years
Factors Considered
- Defender’s Advantage: The defender (VoiceKey system) requires minimal compute resources compared to the attacker.
- Technological Advances: Assume that both attackers and defenders have access to the latest technologies.
- Resource Allocation: Attackers cannot feasibly use all global compute power.
Bypass Probability Estimates
-
At 1 Year
- Attacker’s Compute: Up to ( 1 \times 10^{17} ) FLOPS (10% of global compute).
- Bypass Probability: Very Low
- The computational requirements to replicate the unique human voice features are beyond the attacker’s capacity.
- Estimate: Less than 0.1% chance of successful bypass.
-
At 5 Years
- Attacker’s Compute: Up to ( 1 \times 10^{18} ) FLOPS.
- Bypass Probability: Low
- Slightly increased resources, but the complexity of the VoiceKey system remains a significant barrier.
- Estimate: Approximately 0.5% chance of successful bypass.
-
At 10 Years
- Attacker’s Compute: Up to ( 1 \times 10^{19} ) FLOPS.
- Bypass Probability: Moderate
- Technological advancements may allow attackers to simulate some features.
- Estimate: Around 1-2% chance of successful bypass.
-
At 50 Years
- Attacker’s Compute: Up to ( 1 \times 10^{27} ) FLOPS.
- Bypass Probability: High
- With massive compute resources, attackers could potentially simulate complex human voice features.
- Estimate: 20-30% chance of successful bypass.
-
At 100 Years
- Attacker’s Compute: Up to ( 1 \times 10^{37} ) FLOPS.
- Bypass Probability: Very High
- Near total compute capacity could be leveraged, possibly including quantum computing advancements.
- Estimate: Over 50% chance of successful bypass.
Note: These estimates are speculative and assume current security measures remain static. In reality, security systems will evolve to counter emerging threats.
Implications for VoiceKey Security
Defender’s Computational Advantage
- Minimal Compute Requirement: VoiceKey is designed to require minimal computational resources from the defender.
- Asymmetric Defense: The system’s reliance on hard-to-replicate features creates an asymmetric challenge for attackers.
Strategies for Maintaining Security Over Time
- Continuous Updates: Regularly update the system to incorporate new security measures and counteract advancements in attack methods.
- Adaptive Algorithms: Employ machine learning models that evolve to detect new forms of attacks.
- Quantum-Resistant Protocols: Develop protocols that remain secure even in the presence of quantum computing capabilities.
- Multi-Modal Authentication: Combine voice authentication with other biometric factors to enhance security.
- Community Collaboration: Engage with the global research community to stay ahead of emerging threats.
Conclusion
Over the next 100 years, assuming exponential compute growth, the computational resources available to potential attackers will increase dramatically. While the VoiceKey system is designed to be secure against current and near-future computational capabilities, the probability of bypassing the system increases over longer time horizons.
To maintain security over time, it is essential to:
- Continuously Evolve Security Measures: Adapt and enhance the VoiceKey system to counteract emerging threats.
- Leverage Advanced Technologies: Incorporate quantum-resistant algorithms and advanced detection methods.
- Engage in Global Collaboration: Work with the research community to stay ahead of potential vulnerabilities.
By proactively addressing these challenges, VoiceKey can remain a robust and secure authentication solution well into the future.
References
- Moore, G. E. (1965). Cramming more components onto integrated circuits. Electronics, 38(8).
- Kurzweil, R. (2005). The Singularity Is Near: When Humans Transcend Biology. Viking Press.
- Koomey, J. G. (2011). Implications of Historical Trends in the Electrical Efficiency of Computing. IEEE Annals of the History of Computing, 33(3), 46-54.
- Waldrop, M. M. (2016). More than Moore. Nature, 530(7589), 144-147.
- Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.
- Shor, P. W. (1997). Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM Journal on Computing, 26(5), 1484-1509.
- National Institute of Standards and Technology (NIST). (2016). Post-Quantum Cryptography: Proposed Requirements and Evaluation Criteria. NISTIR 8105.
AI Integrity Alliance
Acknowledgments
We extend our gratitude to the researchers and technologists whose work on computational growth, cryptography, and cybersecurity informs our understanding of future challenges. Their insights are invaluable in shaping the strategies to maintain the security and integrity of authentication systems like VoiceKey over the coming decades.
Note: This document is part of the VoiceKey project by the AI Integrity Alliance. It provides an analysis of compute resource expenditures over the next 100 years, assuming exponential growth, and assesses the bypass probabilities of the VoiceKey system at specified intervals. The projections are intended to inform strategies for maintaining robust security in the face of evolving technological capabilities.