By way of brute-forcing the personal key, each a 12-word seed phrase and a 24-word seed phrase provide the identical degree of safety if they’re generated utilizing a robust random quantity generator.
The explanation for that is that the personal key derived from the seed phrase is basically a 256-bit quantity within the case of the Bitcoin protocol (particularly, the secp256k1 elliptic curve utilized in Bitcoin). The seed phrase is used to deterministically generate the personal key, however the personal key itself has a set size of 256 bits.
When utilizing a 12-word seed phrase, the seed phrase is used to generate the personal key by a sequence of cryptographic operations. Equally, when utilizing a 24-word seed phrase, the identical course of is adopted to generate the personal key.
The additional phrases in a 24-word seed phrase are used to offer extra entropy and enhance the variety of attainable seed phrases. This helps in defending towards the potential of collisions (two completely different seed phrases producing the identical personal key), nevertheless it doesn’t instantly influence the safety of the personal key itself.
In abstract, the safety of the personal key’s decided by the size and randomness of the underlying bits used to generate it, somewhat than the variety of phrases within the seed phrase. Each a 12-word seed phrase and a 24-word seed phrase can present sturdy safety if generated correctly.
