CryptoNight, the pow function used by Monero is such a function. https://monerodocs.org/proof-of-work/cryptonight/ Basically it needs more random memory accesses, and GPU memory is not designed for ...

To compute $kG$ you need $O(log(k))$ operations. (For every bit, double the result and and additionally add $G$ if bit is $1$). As you mentioned in a comment for around $k=1024$ you would need like $... View answer Accepted answer 4 votes Maybe I miss something, but after some quick thoughts about that algorithm, I think it is not secure. Therefore it may not be used and be more like an example for teaching (with no name). The problem ... View answer Accepted answer 3 votes Yes, it is even possible without interaction (nothing Bob needs to send to Alice). The method is called "ring signature". Let's say she wants to sign a message like "I am Alice an ... View answer 3 votes It is totally possible and fairly easy to see without any advanced maths. The curve has order n (n Points in the curve) the private key d is [0... n-1] and the random number k [1... n-1] and there are ... View answer 2 votes You don't need to invert the$f_i$to invert the whole function. You know$L_d$, so you know$R_{d-1}$and the the input of$f_d$. The xor can reverse itself. So you get$L_{d-1}$by simply ... View answer 1 votes This is more an answer to why the uniqueness of the sums effects the size so much that the case for$52485332\$ becomes trivial (its way to long for a comment). When all sums must be unique, then they ...

G is a point on the curve, but multiplication on elliptic curves is not the same as just multiplying the x and y value by the number. Have a look here https://en.m.wikipedia.org/wiki/...

The encryption of the key has nothing to do with RSA. Cracking it is as hard as cracking every other encrypted stuff using the same encryption algorithm (not RSA, because it would be encrypt ...