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.
