If the bit size is 128 bits, I know that BSGS is not possible due to memory issues.

I know that the complexity of Pollard-rho for 128 bits is 2^64.

and I know that it is not possible to do 2 ^ 64 operations on a typical computer.

Is there any other way? do solve 128bit ECDLP when ord(G)=prime number


Yes, Pollard-rho is the best algorithm known for solving hard instances of ECDLP (those where the generator is of prime order).

The current (public) record seems to be order $2^{117.35}$ for sect113r2 by Daniel J. Bernstein, Susanne Engels, Tanja Lange, Ruben Niederhagen, Christof Paar, Peter Schwabe and Ralf Zimmermann in Faster elliptic-curve discrete logarithms on FPGAs (eprint, 2016). Notice that this is for a curve over a binary field, and prime fields are noticeably harder at equal size (because cary-less arithmetic is cheaper).


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