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0 votes

Exponentiation Problem of G2 in MNT curve

I think the print function print H1 and H2 in a different way, you can try print('G1 equals G2:', G1 == G2) print('H1 equals H2:', H1 == H2) the result should show ...
Flying Caps's user avatar
-3 votes

can we modify the prime field by increasing it in secp256k1?

yes its possible, example take prime p=23 parameter of curve x=x^3+ax+b where a=1 b=4 base point (0,2) field of curve is 29. extand curve with p=529 (23x23) , same parameter, you got curve with field ...
knuckballs's user avatar
-4 votes

Can we retrieve his private key using his public key in ECC?

Hello yes you Can recover private Key from pubkey. You need backdoor. Use inverse euclid math (mpz_inv in GCC GNU ). Use modular math fonction . Lot fonction in C++. Knowing how multiply base point. ...
Knuckballs's user avatar
1 vote

Getting the slope of a public key given its x and y coordinates

Since you are talking about ECC and we are in a crypto stack exchange, I suppose you define your elliptic curve over a finite field, lets say $\mathbb{F}_q$. Here is a tool that lets you plot elliptic ...
Alex Them's user avatar
  • 125
1 vote

Example of elliptic curves endomorphism construction

Regarding your need for some basic examples of endomorphisms, I would suggest the book Rational Points on Elliptic curves by Joseph H. Silverman and John T. Tate on chapter 6, Section 4 (Complex ...
Alex Them's user avatar
  • 125
2 votes

Example of elliptic curves endomorphism construction

I am not sure if I understand your question. You can have trivial endomorphisms like multiplication by $n$ maps ([$n$]) or the Frobenius endomorphism, which can be computed easily (see https://www....
honzaik's user avatar
  • 452
1 vote

diffie hellman key exchange compared with ECDH

That sounds interesting and you will learn a lot! I assume you are a student. You should start at the start: "New Directions in Cryptography" - This is a fundamental and well-written paper. ...
Titanlord's user avatar
  • 2,309
1 vote
Accepted

Is the D = D1 + D2 of HECC the equivalent of the P + Q tangent-and-chord method as occurs in ECC?

Any of the Divisors in Mumford's analysis consists of 2 points No, this is true only for curves of genus 2. For curves of genus 3 and more it can be both true and false. This is because the number of ...
madhurkant's user avatar
4 votes
Accepted

Questions related to Hyper Elliptic Curve Cryptography

What do they divide? To be precise, they do not divide anything. Divisors are nothing but a formal sum of points on a curve done with each points appended with an arbitrary integer. Mathematically ...
madhurkant's user avatar
2 votes
Accepted

Finite Fields and security level in HECC (Hyper Elliptic Curve Cryptography)

I was looking at the question from couple of days but refrain from answering for the reasons, as in Para 3. I wouldn’t be able to provide a practical answer but would provide a theoretical one. do I ...
madhurkant's user avatar
1 vote

What’s the fastest known Koblitz curve addition law for FPGA that maximizes the per-LUT throughput?

The question is for curve seckp256k1. That's the elliptic curve of Weierstrass equation $y^2=x^3+a\cdot x+b$ in the finite field $\mathbb F_p$ with $p=2^{256}-\epsilon$, $\epsilon=2^{32}+977$, $a=0$, $...
fgrieu's user avatar
  • 142k
0 votes

How does recovering the public key from an ECDSA signature work?

It is well-known that one can recover the ECDSA public key used from a valid ECDSA signature on a known message, cf. Section 4.6 of https://www.secg.org/sec1-v2.pdf.
Eric Verheul's user avatar
1 vote
Accepted

Is it safe to reuse the same scalar when doing direct scalar multiplication on Koblitz curves?

In the question's context, it's safe to reuse the same scalar when doing direct scalar multiplication on Koblitz (or other elliptic) curves. More precisely: irrespective of how many $(\mathsf{seed},\...
fgrieu's user avatar
  • 142k
1 vote

Is it safe to reuse the same scalar when doing direct scalar multiplication on Koblitz curves?

There are multiple ways in which question can be dealt but I will choose to explain what scalar multiplication is because it will be more natural . Short Answer: No Explanation: In pure terms of ...
madhurkant's user avatar
1 vote
Accepted

SDLog - looking for papers

That is the name the problem is known as. It may also be seen as forging an ECDSA signature without signing queries and having a message such that $H(m) = 1$. See Limits in the Provable Security of ...
Samuel Neves's user avatar
  • 12.6k

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