cryptography – Is it possible to reduce the field size without disrupting generation of public keys?

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i was wondering if its possible to reduce to field to a 130 bit or lower

No, that would be woefully insecure. The security of elliptic curve cryptography scales with the half of the field size. A 133-bit curve would only have 64.5-bit security. That means that with ~264.5 curve operations one can compute the private key for a given public key. This is tiny amount of work for a competent attacker.

without disrupting the actual functionality

Even if it weren’t a terrible idea, this would be an extremely invasive change, requiring the entire ecosystem to adopt and switch to a different, smaller, curve. All Bitcoin software would need to adapt.

As far as I know, there aren’t even any recommended standardized curves with a size below 160 bits.

what i mean by this is the actual generation of secp256k1 public keys should not be disrupted.

If this were possible, the Bitcoin ecosystem would already have embraced it. secp256k1 uses a specific finite field, the integers modulo 2256 – 232 – 977. If you use a different field, it’s a different curve, with different private/public keys and everything.

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