# Questions tagged [elliptic-curve-generation]

ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudorandom generators, and other tasks. they can be used for encryption by combining the key agreement with an asymmetric encryption scheme.

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### The Generator point and Mod P in ECDSA

I've been reading about The discrete logarithm problem as of recent and i decided to try it out on a small portion of numbers myself and i actually came to a mental gridlock after watching this Video....
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### Why is it necessary that the mod in an elliptic curve is a prime? [duplicate]

For the elliptic curve y^2 = x^3+2x+2 mod(23), why is it necessary that 23 is a prime. Why is the elliptic curve y^2 = x^3+2x+2 mod(24) not suitable for elliptic curve cryptography?
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### How are the points in an elliptic curve over the finite field calculated?

For the elliptic curve with equation $y^2 = x^3 + x + 0 \pmod{13}$ in the finite field, how are all the points in this curve calculated. See the image below for an example created via https://graui.de/...
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The SafeCurves project provides a Sage script to verify the SafeCurves criteria for given curves, https://safecurves.cr.yp.to/verify.html According to the description, the script works simply as: $... 2 votes 1 answer 156 views ### Diffie Hellman groups I saw that non-negative integers with the addition operation cannot be the Diffie Hellman group. I'm having trouble understanding why it cannot be the DHKE group. To be DHKE group, there are five ... 1 vote 0 answers 87 views ### Elliptic curve subgroup with$p$elements in field of characteristic$p$Are there any elliptic curves defined over a finite field$\mathrm{GF}(p^k)$with a subgroup of order$p$where the discrete log (and preferably DDH) problem is hard? Elliptic curve with prime ... 1 vote 2 answers 325 views ### How to convert coordinates o a point from y^2=x^3+7 to y^2=x^3+4? [closed] To moderator, this my question is not off topic !!! Please OPEN MY QUESTION. If for this place elliptic curves was off topic this so world is crazy. ... 3 votes 1 answer 293 views ### Significance of y-coordinates in ECDH public key exchange In the research paper Breaking the Bluetooth Pairing – The Fixed Coordinate Invalid Curve Attack? by Biham and Neumann, 2019, they talk about attacks in Bluetooth pairing, they state that in the ... 2 votes 1 answer 216 views ### Calculate a base point on the twist of secp192k1 with maximal order I want to calculate a base point on the twist of secp192k1 with maximal order. ... 1 vote 0 answers 52 views ### How to maintain the width of the cipher image in ECC Image Encryption from Singh and Singh (2015)? I am a beginner in cryptosystems and I hope I would be accepted in the community. I was trying to implement Singh and Singh (2015) ECC image encryption algorithm on Matlab. I have been able to ... 2 votes 1 answer 434 views ### Excluding specific factors for Pohlig-Hellman I want to use Pohlig-Hellman and BSGS to solve the discrete log of an Elliptic Curve which has a composite order generator. The ... 3 votes 1 answer 104 views ### Construction of secure Elliptic Curve subgroup over a much larger field How can we construct an Elliptic Curve subgroup of cryptographic interest out of an Elliptic Curve over a much larger finite field, including the familiar$\Bbb F_p$for prime$p$? The Discrete ... 4 votes 1 answer 237 views ### Probability of a prime number of points on an elliptic curve over a prime field Suppose we have some elliptic curve defined over$\mathbb F_p$, with$p$a large prime. Let$n$be the number of points on the curve. I am interested in what is currently known about the probability* ... 2 votes 0 answers 88 views ### Elliptic curve of order$p = 2q + 1$Does anyone know an example of an Elliptic Curve of caracteristic$p$($E_p$) that has a point generator$G$that generates a subgroup of order$q$, with$p$,$q$being prime numbers and$p = 2q + 1$? 0 votes 1 answer 263 views ### Division of Point in Elliptic Curve: Getting Back Point Let$P=(x_p,y_p)$be a point on elliptic curve$E (a, b) := y^2=x^3+ax+b$, for an integer$n$, there exists a point$Q=(x_q,y_q)=nP$on$E (a, b)$. If$(x_q,y_q)$and$n$are given, what is the ... 1 vote 0 answers 99 views ### Elliptic Curve (Point Counting) I am studying elliptic curves in particular point counting. If I have coordinates P and 2P, is there a way to calculate the total points in between P and 2P using either curve parameters or algorithm? ... 1 vote 0 answers 96 views ### Need help understanding SPAKE2 setup values I am trying to write a simulation of the SPAKE2 protocol in python (just so I can get a better understanding of the protocol altogether). I am reading through the ietf draft here: Datatracker. There'... 0 votes 1 answer 413 views ### Order of subgroups formed by Elliptic Curves with a Cofactor In this question: Why are the lower 3 bits of curve25519/ed25519 secret keys cleared during creation? The answer indicates that the order of all points on the curve over the finite field ... 0 votes 0 answers 66 views ### Difference in elliptic curve order and finite field size [duplicate] Must the prime finite field, Fp, an elliptic curve is defined over always have a greater number of elements than the cardinality of an elliptic curve. For example, If I have ... 1 vote 1 answer 376 views ### Point doubling with only one coordinate In many source codes that implement ECDH, there is a function that multiplies the base point of that curve with a constant. This function usually takes as arguments the constant and just one ... 3 votes 0 answers 174 views ### Check validity of generated parameters for SIDH In section 4.1 of the paper Towards quantum-resistant Cryptosystems From Supersingular Elliptic Curve Isogenies by Feo, Jao and Plût it is described how you generate valid parameters for the SIDH ... 5 votes 1 answer 7k views ### curve25519 by openSSL How can i generate ec curve25519 keys using openSSL? When I run openssl ecparam -name curve25519 -genkey -noout -out private.ec.key I have this message ... 1 vote 1 answer 283 views ### Does any problem arise when the order of an elliptic curve is equal to its prime field modulus? [duplicate] Regarding cryptographic schemes in elliptic curve cryptography, is there a problem with having the order of an elliptic curve being equal to its prime field modulus? That is, an elliptic curve where$...
If we have two elliptic curves $E$ and $E'$ and the points of both elliptic curves are same. Then all the points of $E$ map to all the points of another elliptic curve $E'$. For example $E$ has ...