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5 votes
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Elliptic curve sequences needed for universal forgery

Elliptic Curve Digital Signature Algorithm (ECDSA) admits universal forgery (UF) if the Attacker can solve the equation $$z=\frac{f_{k-1}(x,y)f_{k+1}(x,y)}{f_{k}(x,y)^2},$$ where $k$ is unknown, $f_{k}...
Alexey Ustinov's user avatar
3 votes
0 answers
151 views

determine degree of boolean polynomial given as black box

I searched a lot but couldn't find a good resource that addresses this question. Given a boolean polynomial with $n$ boolean variables as a black box, what is the most efficient way to compute its ...
Math-fort's user avatar
  • 103
1 vote
0 answers
95 views

Reference request: Time and proofs of shared pasts

Is there research about structures for notions of time with distributed systems of information, as with blockchains? I am thinking of tuples $(I, T, P, A, \prec, s, \eta, u)$ where $I$, $T$ and $P$ ...
Gerrit Begher's user avatar
1 vote
0 answers
212 views

Generate algorithmically an elliptic curve with its exact class group structure?

Is it possible to generate an elliptic curve $E$ (randomly), together with knowing its class group $\mathrm{Cl}(\mathcal{O})$ structure? where $\mathcal{O}$ is its endomorphism rings $\mathsf{End}(E)$ ...
Taylor Huang's user avatar
0 votes
0 answers
141 views

State of the art on attempts to solve the elliptic curve discrete logarithm problem through transfering the problem to a weaker curve

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully ...
user2284570's user avatar