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Bitcoin Traders Are Discussing BTC’s Record High, but Quantum Computing Is Threatening the Math Behind It

Bitcoin relies on elliptic curve cryptography (ECC) to secure wallet addresses and validate ownership. But ECC, like RSA, is vulnerable to Shor’s algorithm — a quantum computing method capable of cracking the discrete logarithm problem, the core math behind Bitcoin's private keys.

Updated Jul 18, 2025, 2:19 p.m. Published Jul 18, 2025, 10:55 a.m.
math behind bitcoin

What to know:

  • Quantum computing could break current cryptographic systems within the next decade, posing risks to online banking and blockchain security.
  • A Capgemini report highlights that 70% of large organizations are preparing for post-quantum cryptography, but only 2% of cybersecurity budgets are allocated to this transition.
  • Bitcoin's reliance on elliptic curve cryptography makes it vulnerable to quantum attacks, with over 25% of coins at risk if quantum computers advance.

A new report by Capgemini warns that quantum computing may break the widely used public-key cryptographic systems within the next decade — threatening everything from online banking to blockchain security.

The report did not single out bitcoin , but focused on encryption systems such as RSA and ECC — the same cryptographic primitives that underpin crypto wallets, transaction signatures, and key security in most blockchains.

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Bitcoin relies on elliptic curve cryptography (ECC) to secure wallet addresses and validate ownership. But ECC, like RSA, is vulnerable to Shor’s algorithm — a quantum computing method capable of cracking the discrete logarithm problem, the core math behind bitcoin's private keys.

Capgemini’s findings were based on a survey of 1,000 large organizations across 13 countries. Of those, 70% are either preparing for or actively implementing post-quantum cryptography (PQC) — a new class of algorithms designed to resist quantum attacks.

Yet only 15% of respondents were considered “quantum-safe champions,” and just 2% of cybersecurity budgets globally are allocated toward this transition.

“Every encrypted asset today could become tomorrow’s breach,” the report warned, referring to so-called “harvest now, decrypt later” attacks. These involve stockpiling encrypted data now in hopes that quantum computers can break it later — a real risk for any blockchain with exposed public keys.

In bitcoin’s case, that includes over 25% of all coins, which have revealed their public keys and would be immediately vulnerable if Q-Day — the hypothetical moment quantum machines can break modern encryption — arrives.

Earlier this week, a draft proposal by Bitcoin developer Jameson Lopp and other researchers outlined a phased plan to freeze coins secured by legacy cryptography, including those in early pay-to-pubkey addresses like Satoshi Nakamoto’s wallets.

The idea is to push users toward quantum-resistant formats before attackers can sweep dormant funds unnoticed.

“This proposal is radically different from any in Bitcoin’s history just as the threat posed by quantum computing is radically different from any other threat in Bitcoin’s history,” the authors wrote, as CoinDesk reported.

While the timeline for Q-Day remains uncertain, Capgemini’s report notes that breakthroughs in quantum error correction, hardware design, and algorithm efficiency have accelerated over the past five years. In some scenarios, researchers believe a cryptographically relevant quantum computer (CRQC) could emerge before 2030.

Meanwhile, governments are acting. The U.S. NSA plans to deprecate RSA and ECC by 2035, and NIST has finalized several PQC algorithms like Kyber and Dilithium for public use, Capgemini said.

Cloudflare, Apple, and AWS have begun integrating them, but as of Friday no major blockchain network (i.e. with tokens in the top ten by market capitalization) has made such moves.

As such, bitcoin’s quantum debate remains theoretical and all steps being taken are preemptive. But as institutions, regulators, and tech giants prepare for a cryptographic reset, the math behind crypto’s security may not hold forever.

Read more: Bitcoin Devs Float Proposal to Freeze Quantum-Vulnerable Addresses — Even Satoshi Nakamoto’s

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