The foundation of modern Internet security is built on public-key cryptography, including RSA, ECC, and DH.
For more than 40 years, these algorithms have become de facto standards across almost every industry — finance, telecommunications, mobile, digital signatures, national defense, and more.
All of this, however, has relied on a single premise:
“On classical computers, deriving the private key from the public key
is computationally infeasible within a valid time window.”
The problem is that this premise no longer holds true.
Quantum computing introduces a fundamentally different computational paradigm that undermines the foundations of existing cryptographic systems — and at the center of this threat lies Shor’s Algorithm.
1. The “Hard Problems” That Classical Cryptography Depends On
In other words, cryptography has long asserted:
“Solving these problems would take billions of years
on classical computers — therefore they are secure.”
But this notion of “hardness” only applies under classical computing assumptions.
Quantum computers approach these problems using a completely different computational framework.
2. Shor’s Algorithm — A New Kind of Mathematics That Breaks Classical Cryptography
Since its publication in 1994, Shor’s Algorithm has been regarded as one of the most disruptive breakthroughs in cryptography and computer science.
Its core mechanism can be summarized as follows.
① Transforming factorization into a “period-finding problem.”
Instead of performing factorization directly,
Once r is obtained, the prime factors p and q that compose N can be derived.
② Using the Quantum Fourier Transform (QFT) to compute r in polynomial time
In classical computing, finding r requires enormous iterative computation.
However, by leveraging
the QFT enables r to be computed in polynomial time.
This is where quantum computing fundamentally changes the game.
③ Once r is known, the factors are automatically revealed
By computing
, andthe GCD with N
the values of p and q are exposed.
This process operates at a speed unimaginable in classical mathematics.
3. How Much Faster Is It in Practice?
Algorithm
| Classical Computing Complexity
| Quantum Computing (Shor) |
RSA Factorization
| Exponential time (effectively infeasible)
| Polynomial time (feasible)
|
ECC DLP
| Exponential time
| Polynomial time |
The conclusion is clear:
Once quantum computing reaches a sufficient qubit scale,
Both RSA and ECC will be broken.
4. “When” It Breaks Is Not the Real Issue — The Attacks Have Already Begun
Adversaries are already using the following strategy:
✔️ HNDL (Harvest Now, Decrypt Later)
Steal today’s encrypted traffic, backups, and stored data
Preserve it for long-term storage
Decrypt everything later once quantum computing becomes practical
This is especially dangerous because
national security
government archives
financial records
healthcare data
can retain strategic value for 10–20 years.
Meaning:
Damage is already underway,
even before quantum computing is fully realized.
5. Conclusion — Every Industry Now Stands at a Quantum Security Turning Point
Today’s industrial ecosystem —
all operate on top of RSA/ECC-based authentication and signature systems.
Quantum computing invalidates that foundational assumption.
Therefore,
The quantum threat is not merely a technical issue —
It is a matter of industrial and national resilience.
In the next post, we will explore the world after Shor’s Algorithm:
How quantum computing disrupts real-world industrial structures,
its impact on authentication and key-management systems, and what this means for security architectures moving forward.
| CMO(Chief Marketing Officer), ICTK CTO(Chief Technical Officer), ICTK Director, Cisco Systems Korea Developer, SK Teletech |
Read more
The foundation of modern Internet security is built on public-key cryptography, including RSA, ECC, and DH.
For more than 40 years, these algorithms have become de facto standards across almost every industry — finance, telecommunications, mobile, digital signatures, national defense, and more.
All of this, however, has relied on a single premise:
The problem is that this premise no longer holds true.
Quantum computing introduces a fundamentally different computational paradigm that undermines the foundations of existing cryptographic systems — and at the center of this threat lies Shor’s Algorithm.
1. The “Hard Problems” That Classical Cryptography Depends On
RSA is based on the hardness of integer factorization.
ECC relies on the hardness of the Discrete Logarithm Problem (DLP).
In other words, cryptography has long asserted:
But this notion of “hardness” only applies under classical computing assumptions.
Quantum computers approach these problems using a completely different computational framework.
2. Shor’s Algorithm — A New Kind of Mathematics That Breaks Classical Cryptography
Since its publication in 1994, Shor’s Algorithm has been regarded as one of the most disruptive breakthroughs in cryptography and computer science.
Its core mechanism can be summarized as follows.
① Transforming factorization into a “period-finding problem.”
Instead of performing factorization directly,
The algorithm analyzes expressions of the form
Once r is obtained, the prime factors p and q that compose N can be derived.
② Using the Quantum Fourier Transform (QFT) to compute r in polynomial time
In classical computing, finding r requires enormous iterative computation.
However, by leveraging
quantum superposition and
interference
the QFT enables r to be computed in polynomial time.
This is where quantum computing fundamentally changes the game.
③ Once r is known, the factors are automatically revealed
By computing
the GCD with N
the values of p and q are exposed.
This process operates at a speed unimaginable in classical mathematics.
3. How Much Faster Is It in Practice?
The conclusion is clear:
Once quantum computing reaches a sufficient qubit scale,
Both RSA and ECC will be broken.
4. “When” It Breaks Is Not the Real Issue — The Attacks Have Already Begun
Adversaries are already using the following strategy:
✔️ HNDL (Harvest Now, Decrypt Later)
Steal today’s encrypted traffic, backups, and stored data
Preserve it for long-term storage
Decrypt everything later once quantum computing becomes practical
This is especially dangerous because
national security
government archives
financial records
healthcare data
can retain strategic value for 10–20 years.
Meaning:
Damage is already underway,
even before quantum computing is fully realized.
5. Conclusion — Every Industry Now Stands at a Quantum Security Turning Point
Today’s industrial ecosystem —
Finance
Telecommunications
Automotive
Energy
Aerospace and defense
Manufacturing and Infrastructure
all operate on top of RSA/ECC-based authentication and signature systems.
Quantum computing invalidates that foundational assumption.
Therefore,
The quantum threat is not merely a technical issue —
It is a matter of industrial and national resilience.
In the next post, we will explore the world after Shor’s Algorithm:
How quantum computing disrupts real-world industrial structures,
its impact on authentication and key-management systems, and what this means for security architectures moving forward.
CMO(Chief Marketing Officer), ICTK
CTO(Chief Technical Officer), ICTK
Director, Cisco Systems Korea
Developer, SK Teletech
Read more
Tech for Quantum
The Era of QAAS (Part 1): Why We Are Facing a "New Age of Threats"
The Era of QAAS (Part 2): Case Studies of Converged Cyber Threats