## Bitcoin and the Shor Algorithm: Why the Current Threat Is a Public Key Issue, Not Encryption

Most discussions about the quantum threat to Bitcoin are based on a fundamental terminological misunderstanding. Encryption in Bitcoin practically does not exist – the blockchain is a public ledger where anyone can see transactions, amounts, and addresses. What truly protects funds are digital signatures (ECDSA and Schnorr) and hash functions, not encrypted text. The real quantum risk is the possibility of forging authorization by deriving a private key from a public key exposed through the Shor algorithm.

## Where the Vulnerability Really Lies: Key Exposure and Taproot Design

Bitcoin's security depends on whether the public key is visible on the blockchain. Many address formats commit to hashing the public key, meaning the raw key remains hidden until a transaction is issued. This narrows the window of opportunity for potential attackers. However, Taproot (P2TR) changes this pattern – it includes a 32-byte modified public key directly in the output, instead of its hash, according to BIP 341.

Project Eleven, an open project monitoring Bitcoin encryption and security, performs weekly scans for exposed public keys. Their public tracker identifies about 6.7 million BTC on addresses that meet criteria for quantum attack exposure. This does not mean an immediate threat, but it shows that the vulnerable pool is measurable and already being tracked today.

## Quantum Computers Need Billions of Physical Qubits – And That’s Not Close

The computational perspective shifts the outlook. To compute the discrete logarithm of a 256-bit elliptic curve ECC, approximately 2300 logical qubits are theoretically needed (according to Roetteler et al.). The problem arises in converting this to error-corrected machines.

Estimates range from 6.9 million to 13 million physical qubits to break a key within an hour to a day, depending on assumptions about error rates and architecture. IBM recently discussed a path toward an error-tolerant system around 2029, but this remains a projection, not a reality. Current quantum computers are very far from this.

## Address Reuse and Signature Migration: Real Challenges

The real issue is not technical – it’s more about migration challenges. If a public key appears on the blockchain, future inflows to the same address remain exposed. Wallet designers can reduce this risk through address rotation, but many users do not adopt such practices.

NIST has standardized post-quantum primitives (ML-KEM/FIPS 203), and BIP 360 proposes a new output type “Pay to Quantum Resistant Hash". The problem: post-quantum signatures are several kilobytes in size, not tens of bytes. This changes the economics of transaction weight, fees, and user experience – posing a bigger challenge than cryptography itself.

## Summary: Infrastructure, Not an Immediate Crisis

Bitcoin encryption is not threatened by quantum computers in the traditional sense. Instead, the network faces a long-term migration challenge related to signatures, public key exposure, and wallet management. Measurable elements – such as the current state of UTXOs with exposed keys, user behavior, and the network’s ability to adopt quantum-resistant solutions – will determine the timeline and success of the transition. This is not a five-minute game but a multi-year infrastructure transformation.