Quote from: pooya87 on Today at 05:53:50 AM

Quote from: jubalix on Today at 03:20:07 AM

The known 2048 words at 128 = 2^128 and IF (and its a big if) there was a sufficently large qbit computuer, becomes 2^64 problem that is a lot more crackabble.

Why did you halve that?

On elliptic curve, a 256-bit private key provides half the security meaning 128 bits of security. But when you have an entropy for key derivation, that entropy is providing the same amount of security as its size. Meaning a 128 bit entropy provides 128 bits of security not 64.

If quantum computers eventually become practical with sufficient qubits, many classical cryptographic problems could be solved much faster. For instance:

- Shor’s algorithm, quantum computers can break ECC and RSA in polynomial time, dramatically reducing their effective security.
-Grover’s algorithm, the security of symmetric encryption schemes would effectively be halved, meaning a 128-bit symmetric key would provide only 64 bits of security against quantum attacks.

I am theorising how you get to the specific key from 2048 known words must be easier than unknown words to get to a specific key in a key space, the entropy might be the same, but the your looking at a different sector of the key space.

The process of deriving a specific key from a constrained set of inputs, such as the 2048 known words in the BIP39 word list used for cryptocurrency wallets, may reduce the practical difficulty of a brute-force attack. Although the theoretical entropy of the system remains unchanged, the search space is effectively constrained.

Think of it like using a lightouse searchlight. If you’re looking for a target in a completely dark area, the light could shine in any direction, covering the entire 360-degree field. However, if you know the target can only be located within a specific arc—let’s say between points A and B—the searchlight doesn’t have to scan the whole field. Even though the target is still hidden, the process becomes more efficient because you’re focusing on a smaller, defined area.

Similarly, knowing that a key is derived from a deterministic process, like a BIP39 word list, limits the search to a specific subset of the key space.