Shor's Algorithm and the Quantum Threat

Shor's algorithm, published by Peter Shor in 1994, proves that quantum computers can break most current cryptography in polynomial time. This is why the SynX quantum-resistant wallet uses post-quantum algorithms.

What Shor's Algorithm Does

Shor's algorithm efficiently solves two problems:

• Integer Factorization: Breaking RSA encryption
• Discrete Logarithm: Breaking Diffie-Hellman and ECDSA

Classical vs. Quantum Complexity

Note the asymmetry: RSA-2048 and ECDSA-256 are different targets with different costs, and Bitcoin sits on the cheaper one. The March 2026 work by Google Quantum AI with the Ethereum Foundation and Stanford compiled two circuits — 1,200 logical qubits with 90 million Toffoli gates, and 1,450 logical qubits with 70 million — both finishing fast enough in principle to take a pending transaction before it confirms. An independent Caltech and Oratomic analysis put the same job at roughly 26,000 physical qubits on neutral-atom hardware over about ten days. The older figure of roughly 2,330 logical qubits (Roetteler et al., 2017) is superseded.

Cryptocurrencies at Risk

How the Attack Works

For ECDSA (used by Bitcoin/Ethereum):

1. Public key is point P on elliptic curve
2. Private key k satisfies: Public = k × Generator
3. Shor's algorithm finds k from the public key
4. Attacker can now forge signatures and steal funds

Timeline to Threat

The credible window for a cryptographically relevant quantum computer is 2029-2033:

• 2029: IBM's Starling targets roughly 200 logical qubits and 100 million gates; Google aims at the same year. A target, not a guarantee — and short of the ECDSA threshold
• 2033: IBM's Blue Jay targets over 2,000 logical qubits on roughly 100,000 physical qubits, comfortably past the 1,200-1,450 needed to break secp256k1
• Today: the best public hardware runs about 2,500 physical qubits, none fault-tolerant at scale. Google's Willow (105 qubits, December 2024) proved the decisive point — below-threshold error correction, where adding qubits makes the machine more stable, not less

Why Migrate Now?

Reasons not to wait:

• "Harvest now, decrypt later": Data intercepted today can be broken when quantum computers arrive
• Blockchain permanence: Transaction signatures are stored forever
• Migration complexity: Better to prepare before crisis

How SynX Resists Shor's Algorithm

The SynX quantum-resistant wallet uses algorithms Shor's cannot break:

• Kyber: Based on lattice problems, not factoring/discrete log
• SPHINCS+: Based on hash functions, no algebraic structure
• No known quantum algorithm threatens these approaches

Frequently Asked Questions

When will quantum computers run Shor's algorithm?

Not precisely known, but the arithmetic is no longer vague. Current public machines reach about 2,500 physical qubits with no fault tolerance at scale. Breaking Bitcoin needs 1,200-1,450 error-corrected logical qubits, which fits inside fewer than 500,000 physical qubits — a machine IBM's roadmap approaches between Starling in 2029 and Blue Jay in 2033.

Will I lose my Bitcoin when quantum computers arrive?

If you haven't moved to quantum-resistant storage, possibly. The SynX quantum-resistant wallet provides protection now.