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Why is the ECDSA cryptography used by Bitcoin considered vulnerable to future quantum attacks?
ECDSA (Elliptic Curve Digital Signature Algorithm) is the digital signature algorithm that secures transactions in Bitcoin, and it is also widely used in financial systems, governments, and technology platforms. Its security relies on the computational difficulty of solving the discrete logarithm problem on elliptic curves.
It is believed that with quantum computing, algorithms like Shor could break this security in reasonable time frames, allowing an attacker to compute the private key from a public key. Although there are currently no quantum computers at that scale, security experts consider it prudent to anticipate.
Bitcoin, by exposing public keys when spending funds, may be leaving a record of public keys available for future attacks, even if they are not vulnerable today.
In this regard, the author of the network improvement proposal indicated that: “The security of ECDSA, and its elliptic curve secp256k1, is based on the practical difficulty of deriving a private key from a public key, as doing so requires solving a mathematical problem known as the discrete logarithm problem on elliptic curves. For a traditional computer, this would take approximately 10⁷⁷ years (that is, a 1 followed by 77 zeros), making it practically impossible.”
“However, quantum computers could run an algorithm called Shor's algorithm, which would allow for efficient finding of the discrete logarithm of a public key on an elliptic curve. Depending on how many qubits (the basic unit of quantum computers, analogous to bits in classical computers) it has, a quantum computer could derive a private key from a public one in a time range that goes from days to seconds,” he assured.
