Two new cryptographic breakthroughs raise concerns over the future of Bitcoin (BTC) and other cryptocurrencies, according to Ledger Chief Technology Officer Charles Guillemet.
According to Guillemet’s Oct. 30 post on X, a recent study shows that it might be easier to break the mathematics behind elliptic-curve cryptography (ECC), which is how Bitcoin is secured.
“Thought it was a bad week for crypto? You may have missed the real news,” wrote Guillemet.
New challenge for elliptic-curve cryptography
First, researchers at Ruhr University Bochum and the Max Planck Institute for Security and Privacy have published a new study called “A Subexponential Time Algorithm for Elliptic Curve Discrete Logarithm.”
Elliptic-curve cryptography works by making it practically impossible to solve the elliptic-curve discrete logarithm problem.
The best general method to solve it so far has been Pollard’s rho algorithm. Its computational cost increases exponentially with key size.
Now, the researchers have presented a subexponential algorithm that might in theory solve it more efficiently.
There is a big caveat. It relies on another claim by OpenAI researchers that requires further investigation.
The new algorithm doesn’t put current cryptographic schemes at risk, Guillemet insisted.
The best attacks for popular curves, like secp256k1 for Bitcoin, NIST P-256 and Ed25519, are still based on Pollard’s rho.
The new one would only be more efficient for hypothetical curves of very large sizes. For now, it’s just theoretical.
More efficient quantum computing attacks on elliptic-curve crypto could break Bitcoin sooner
The second breakthrough is a big advance in the efficiency of quantum computing attacks on elliptic-curve cryptography.
Guillemet referenced a public research project, ECDSA.fail, aimed at improving the efficiency of quantum computing attacks against elliptic-curve digital signatures.
Researchers managed to reduce the estimated quantum circuit cost by about 70% relative to what Google previously reported, the Ledger executive explained.
Current estimates put the cost at about 0.91 billion in the logical-qubit-times-Toffoli-gates metric, down from 2.99 billion in Google’s figures.
What’s more important is that the French quantum computing company Alice & Bob has published a new paper estimating that it’s theoretically possible to break Bitcoin’s secp256k1 cryptography using fewer than 30,000 physical cat qubits in about an hour.
The same paper estimates that factoring RSA-2048 would require 22,593 cat qubits and take about 3.14 days.
Of course, these numbers are for a very advanced fault-tolerant quantum computer that doesn’t exist yet.
Such a quantum computer does not exist, so there is no immediate risk to Bitcoin, Guillemet noted.
However, these findings are a reminder of how the estimated resources needed to break common cryptographic schemes keep shrinking.
