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4 votes

Why is discrete logarithm not quantum proof?

The problem is by definition modular, and the equation is $$g^x\equiv h \pmod p$$ for the integer case. This equation a single solution since the map $x \mapsto g^x \pmod p$ is one to one. Thus there ...
kodlu's user avatar
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3 votes

RSA like problem with unknown e and d

If I understand correctly, it's a DLP (Discrete Logarithm Problem) to find that value. I may make it somewhat easier if I try to solve the DLP for p and q respectively, but for ~500 bits, it's still a ...
poncho's user avatar
  • 148k
2 votes
Accepted

Given a random point on a curve defined over a prime field, is it possible to compute 2 different scalar that will lead to the same result?

Consider an Edwards curve with equation $x^2+y^2=d\,x^2y^2$ in the field $\mathbb F_p$, with prime $p\bmod 4=1$, integer $d$ with $d^{(p-1)/2}\bmod p=p-1$. The group law is $$\bigl(x_1,y_1\bigr)+\bigl(...
fgrieu's user avatar
  • 142k
2 votes

Given a random point on a curve defined over a prime field, is it possible to compute 2 different scalar that will lead to the same result?

does 2 scalars $S1$ $S2$ exist such as $packed(S1\cdot P)= packed(S2\cdot P$) $S1 = S2$ is equivalent to the statement that $S1 - S2$ is an integer multiple of the order of $P$. $S1 \ne S2$ If ...
poncho's user avatar
  • 148k
1 vote

Is MOV attack against ECDLP fundamentally impossible?

Actually, the multiplicative group of the extension field $GF(p^k)$ does have order $p^k-1$. You appear to be confusing that with the multiplicative group $\mathbb{Z}_{p^k}^*$. That does have order $...
poncho's user avatar
  • 148k
1 vote
Accepted

Is discrete logarithm good approach for a time-bounded proof of work?

There will still be variability around the mean for using DL. More importantly, the strength you get by choosing $x$ in $[1,x_{max}]$ is of the order $\log(\sqrt{x_{max}})=\frac{1}{2} \log x_{max}$ (...
kodlu's user avatar
  • 22.8k
1 vote

Why is discrete logarithm not quantum proof?

The input and output are all over a finite field. There is no need to find a specific value. We find the value mod p, which as you say can be viewed as an infinite collection of natural numbers all ...
Meir Maor's user avatar
  • 11.8k

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