Cryptography in the quantum age

Quantum vs. Crypto Why some locks shatter & others hold

Quantum computers threaten the math behind your encrypted messages. But not all cryptography is equally vulnerable. Scroll to find out why.

scroll
Elliptic Curve Cryptography

A beautiful structure to exploit

ECC relies on a deceptively simple idea: take a point on an elliptic curve and "multiply" it by a huge secret number. Going forward is easy. Reversing it — the discrete logarithm problem — is astronomically hard for classical computers.

But "hard" is not "impossible." The security depends entirely on the algebraic structure of the curve — a structure that quantum algorithms can detect and dismantle.

Elliptic curve point addition — the trapdoor function behind ECC
The quantum attack

Shor's algorithm shatters the curve

Peter Shor's 1994 algorithm uses quantum superposition to find hidden periods in mathematical functions — the same periodic structure that makes ECC work.

A quantum computer can solve the elliptic curve discrete logarithm in polynomial time, reducing a problem that would take classical computers billions of years to mere hours.

1 Place all possible answers in superposition simultaneously
2 Apply modular exponentiation to entangle input & output registers
3 Quantum Fourier Transform reveals the hidden period
4 Period → secret key. The curve's structure is fully exposed
Input bits avalanche through irreversible compression — no structure survives
Cryptographic Hash Functions

Designed to be structureless

Hash functions like SHA-256 are deliberately engineered to destroy all mathematical structure. Every bit of input causes an unpredictable avalanche through the entire output.

There is no hidden period. No algebraic group. No exploitable pattern. The output is designed to be indistinguishable from random noise.

The best quantum can do

Grover's algorithm: a modest speedup

Without structure to exploit, the best quantum attack on hashes is Grover's algorithm — an unstructured search that amplifies the probability of finding the right answer.

Grover provides only a quadratic speedup: searching 2256 possibilities becomes 2128. That's still an incomprehensibly large number — far beyond any foreseeable quantum computer.

Grover's search: checking cells one quantum step at a time. Faster, but no shortcut.

Side by side

Structure is the difference

Quantum-vulnerable

Elliptic Curve Crypto

  • Based on algebraic group structure
  • Relies on discrete log being hard
  • Shor's finds hidden period in structure
  • Exponential speedup → broken
  • 256-bit key → effectively 0 bits security
Quantum-resistant

Hash Functions

  • No algebraic structure to exploit
  • One-way avalanche destroys patterns
  • Grover's: brute-force search only
  • Quadratic speedup → manageable
  • 256-bit hash → still 128 bits security
2128 ops
Classical attack on ECC
poly(n)
Quantum attack on ECC
2256 ops
Classical attack on hash
2128 ops
Quantum attack on hash
The takeaway

Quantum computers exploit structure,
not raw speed

Shor's algorithm doesn't try every key. It detects the hidden mathematical scaffolding that makes public-key cryptography work — and uses it to find the secret key directly.

Hash functions survive because they were built to have no scaffolding. The best a quantum computer can do is search a little faster through an impossibly large space.

This is why post-quantum cryptography replaces ECC with lattice-based or hash-based schemes — problems where quantum computers find no structure to grab onto.

View on GitHub →