Why Quantum Computing Will Break Modern Cryptography 

Quantum computing is often described as a future threat to encryption. The common explanation is that quantum computers will become so powerful that today’s encryption will no longer be able to withstand them. 

That is directionally correct, but it misses the most important part of the story. 

Quantum computers do not threaten modern cryptography simply because they are faster computers. They threaten it because some of the mathematical problems that today’s cryptography depends on become fundamentally easier to solve using quantum algorithms. 

Much of modern cybersecurity relies on mathematical problems that are easy to perform in one direction but extraordinarily difficult to reverse. Public-key cryptography works because, with today’s computers and algorithms, solving those problems would require an impractical amount of computation or time. 

Quantum computing changes that assumption. 

Public-Key Cryptography Depends on Hard Mathematical Problems 

Modern cryptography does not generally depend on keeping its algorithms secret. RSA is public. Elliptic-curve cryptography is public. Researchers and adversaries can know exactly how the algorithms work. Their security comes instead from the difficulty of solving particular mathematical problems. 

These problems are (mostly) mathematical one-way streets. Going in one direction is relatively easy. Going backward is extremely difficult. 

For example, multiplying two numbers is easy: 

61 × 53 = 3,233 

Going backward and determining that 3,233 is the product of 61 and 53 is still easy because the numbers are small. 

Now imagine doing the same thing with a number hundreds of digits long that was created by multiplying two enormous prime numbers. Finding those original primes becomes dramatically harder, which is the foundation of RSA encryption. 

Elliptic-curve cryptography uses a different mathematical problem (the Elliptic Curve Discrete Logarithm Problem (ECDLP)), but the same basic concept applies. Performing a particular operation is straightforward. Reversing it without knowing the secret value is computationally infeasible. 

Today’s public-key cryptography therefore depends on an important assumption: 

Some mathematical problems are so difficult for classical computers that an attacker cannot solve them within a useful amount of time.  Quantum computing threatens that assumption. In 1994, mathematician Peter Shor developed a quantum algorithm that can efficiently solve both integer factorization and discrete logarithm problems. Those are precisely the problems protecting most of today’s public-key cryptography. That is why the impact is so significant. 

Exactly What Breaks? 

Not every type of cryptography is affected equally. 

Public-key algorithms based on integer factorization or discrete logarithms face the greatest threat because Shor’s algorithm directly attacks the mathematical problems that make them secure. 

Symmetric cryptography and cryptographic hashing are affected differently. 

Cryptography	Common Examples	What It Relies On	Quantum Impact
Public-key encryption	RSA	Integer factorization	Broken by Shor’s algorithm
Key exchange	Diffie-Hellman	Discrete logarithm	Broken by Shor’s algorithm
Key exchange	ECDH / ECDHE	Elliptic-curve discrete logarithm	Broken by Shor’s algorithm
Digital signatures	RSA signatures	Integer factorization	Broken by Shor’s algorithm
Digital signatures	DSA	Discrete logarithm	Broken by Shor’s algorithm
Digital signatures	ECDSA	Elliptic-curve discrete logarithm	Broken by Shor’s algorithm
Symmetric encryption	AES-128, AES-192, AES-256	Secret-key search	Potentially weakened by Grover’s algorithm, not broken like RSA or ECC
Cryptographic hashing	SHA-256, SHA-384, SHA-512, SHA-3	One-way hash properties	Affected by quantum search techniques, but not fundamentally broken
Post-quantum key establishment	ML-KEM	Module-lattice problems	Designed to resist known quantum attacks
Post-quantum signatures	ML-DSA, SLH-DSA	Module-lattice / hash-based problems	Designed to resist known quantum attacks

NIST specifically identifies current public-key systems based on integer factorization and discrete logarithms as vulnerable to a sufficiently capable quantum computer. 

The reason becomes clearer when looking at RSA and elliptic-curve cryptography separately. 

Why This Becomes a Cybersecurity Problem 

The phrase “quantum computers will break encryption” can actually understate the problem. Public-key cryptography does much more than encrypt information. 

It helps answer some of cybersecurity’s most fundamental questions: 

Who am I communicating with? 

Can I trust this system? 

Has this information been modified? 

Did this software really come from the organization claiming to have created it? 

Public-key cryptography supports technologies including: 

• TLS and HTTPS 

• VPNs 

• SSH 

• PKI and digital certificates 

• Digital signatures 

• Code signing 

• Secure software updates 

• Device authentication 

• Machine identities 

• Secure email 

When you visit an HTTPS website, the actual data flowing between your browser and the website will often be encrypted using a symmetric cipher such as AES. AES itself is not the major quantum vulnerability. However, around it, a modern TLS connection may us elliptic-curve cryptography to securely establish the symmetric encryption keys used for the session. Certificates and digital signatures are also used to authenticate the server and prove that the browser is communicating with the intended system. 

A simplified version looks something like this: 

1. Browser connects to server 

2. Server proves its identity using a certificate and digital signature 

3. Browser and server perform a public-key key exchange 

4. Both sides establish a shared symmetric key 

5. AES or another symmetric cipher encrypts the actual application traffic 

Today, an attacker observing this exchange cannot simply derive the private cryptographic values protecting it… but a cryptographically relevant quantum computer changes that. 

If the key exchange depends on Elliptic Curve Diffie-Hellman, Shor’s algorithm attacks the elliptic-curve discrete logarithm problem. If the authentication mechanism relies on an RSA or ECDSA signature, those algorithms are vulnerable as well. 

So the concern is not so much quantum computers can “break AES.” AES may still be perfectly usable. The mechanisms used to establish the AES key and establish trust between the systems are what must change. 

If an attacker could recover a private signing key, the problem moves from confidentiality to integrity and authentication. 

Potential consequences include the ability to: 

• Impersonate trusted systems 

• Defeat certain authentication mechanisms 

• Forge digital signatures 

• Undermine digital certificates 

• Compromise secure communications 

• Potentially sign malicious software as though it came from a trusted publisher 

The cryptographic infrastructure used to establish digital trust would have to be replaced.  

The risk begins before the quantum computer arrives too. The immediate confidentiality concern commonly called Harvest Now, Decrypt Later. They can capture encrypted information now, retain it, and decrypt it later if sufficiently powerful quantum capabilities become available. That creates a particular concern for government, defense and critical infrastructure environments where information may need to remain confidential for many years.