Security of Bitcoin: Analyzing the secp256k1 Discrete Logarithm Vulnerability

I show how the Baby-step / Giant-step (BSGS) algorithm attacks the discrete-log on secp256k1, then walk through whether modern supercomputers (or quantum machines) could realistically break Bitcoin — and why Bitcoin’s curve remains secure for the foreseeable future.

In this video, you’ll get:

🔎 A short, intuitive explanation of Baby-step / Giant-step and why it uses a square-root time/space tradeoff: solving a discrete log in a group of size n takes about O(√n) time and memory.

🧮 What that means for secp256k1 (group order ~2²⁵⁶) → a naive BSGS attack needs on the order of 2¹²⁸ steps (and corresponding memory), which is astronomically large in practice.

🖥️ A realistic assessment of classical supercomputers: even massively parallel classical hardware only reduces constants — they don’t change the √n barrier. The storage + computation demands for 2¹²⁸-class attacks are outside feasible engineering limits today.

⚛️ Quantum computers may never be realised and are not a threat for the foreseeable future

✅ Conclusion: With current classical and near-term quantum technology, breaking secp256k1 is not practically feasible — Bitcoin’s cryptographic assumptions remain secure over the foreseeable future.