Elliptic curves are a mathematical structure. In cryptography, it is common to use the structure $y^2 = x^3 + ax^2 + b$ over a finite field. Questions relating to elliptic curves and derived algorithms should use this tag and might also consider specific tags such as discrete-logarithm and ecdsa.

learn more… | top users | synonyms (1)

2
votes
2answers
108 views

Why are some $x$ coordinates unsuitable for an ECDSA generator point?

For Bitcoin's ECDSA curve (secp256k1, where $a=0$, $b=7$), why can't the generator point's first coordinate be $x=0$? That is, the point on the curve would be $(0,y)$ where $y$ satisfies $y^2 = 0^3 + ...
3
votes
1answer
93 views

Isn't the security of EC curve 25519 126 bits?

The security of the EC25519 is given as 128 bits, but since the order of the group is 252 bits shouldn't the security be 126 bits? Given as half the magnitude of the underlying field, since DLP ...
0
votes
0answers
5 views

Point of elliptic curve [migrated]

How can we calculate the multiple of a point of an elliptic curve? For example having the elliptic curve $y^2=x^3+x^2-25x+39$ and the point $P=(21, 96)$. To find the point $6P$ is the only way to ...
0
votes
2answers
90 views

What is a good way to demonstrate elliptic curve cryptography?

For school (high school) I am writing an essay on elliptic curve cryptography. The assignment needs to include a practical part, so I decided to write a Python class for elliptic curves. This class is ...
7
votes
1answer
261 views

How does ECDH arrive on a shared secret?

I read a brilliant, three part article on Elliptic Curve cryptography (one, two, three). It was able to explain Elliptic Curves to me in a way that didn't require a math degree to understand. The ...
0
votes
1answer
59 views

C# implementation of curve25519 to ed25519 conversions [closed]

WRT the selected answer here: Can curve25519 keys be used with ed25519 keys? Is there any c# implementation of this or equivalent? Thanks.
2
votes
2answers
138 views

Solving Quadratic equations in Galois Field (2^163)

Hello I am working on implementing a message to elliptic curve point mapping hardware circuit I have done some research and found out the koblitz mapping method: I will be using a field of binary ...
3
votes
2answers
145 views

Which multiplicatively homomorphic encryption scheme supports encryption of 0?

I want a multiplicatively homomorphic encryption scheme that supports encryption of 0 (e.g. Elgamal doesn't support). I also want the multiplication to be operated on the ciphertext of 0, i.e., if ...
0
votes
0answers
38 views

request for data to test deterministic ecdsa signature algorithm for secp256k1

I’m implementing the RFC 6979 procedure to compute a message signature. I want to test my program on the secp256k1 elliptic curve. Note the “k” in secp256k1, i.e. the Koblitz curve. If you have the ...
1
vote
1answer
84 views

Polynomial division hardware implementation

I am beginning the implementation of the polynomial binary division algorithm now as I understood i will be checking the MSB bit if 1 to XOR and shift the sum if 0 i will only shift. What I am not ...
0
votes
0answers
62 views

processing time for multiplication and exponentiation in pairing base cryptography

I'm using the Boneh-Boyen-Shacham signature scheme and want to estimate complexity in my scheme. As reported in "Scott M., Efficient Implementation of Cryptographic pairings", if we set parameters ...
0
votes
0answers
49 views

Polynomial Inversion over Galois Field

Hello guys I am looking to calculate the Inverse of a given polynomial in Galois field I have found the little Fermat's algorithm and the Itoh-Tsujii I am getting a bit confused with both algorithm ...
2
votes
1answer
88 views

Roots in modulo field

I have a point $(X,Y)$ on an elliptical curve $E(a,b)$ where $a=-3$ and $B$ is a large number that is in hexadecimal from -51BD. To compress this point oficially in a program, we know that every $X$ ...
1
vote
1answer
31 views

Modulo Square Roots [duplicate]

Here's my issue and someone can help me understand it so I can program it correctly. I have a point(X,Y) on an Elliptical Curve E(a,b) where a=-3 and B is a large number that is in hexidecimal from ...
1
vote
2answers
95 views

Point decompression on an elliptic curve

I'm programming an elliptic curve cryptosystem and I'm having difficulty with decompressing points. The following information is from my project specification as to my understanding: Given a point ...
0
votes
0answers
50 views

Find generator for irreducible polynomial over binary field

I read this tutorial and I have following question. How they assume that generator: g = (0010) is correct for this polynomial and how to choose the best generator from all for the field.
1
vote
1answer
124 views

Creating serial key generator using ECDSA, how to get signature short enough?

I've written some questions in this stackoverflow and got great responses but now I'm trying to wrap it all together. I have for the last couple of weeks been building a serial key generator project ...
0
votes
0answers
31 views

how can I change representation of point to Jacobian coordinates in Edward's Curve

I want to simulate this algorithm but I want to change it's output to Jacobian coordinates. what should I do ? In the other way how can we change extended homogeneous coordinates to Jacobian ...
1
vote
1answer
81 views

ECC - ElGamal with Montgomery or Edwards type curves (curve25519, ed25519) - possible?

I know the usual way of using getting shared secrets for encryption with ECC is DH, however, this only works with two keypairs of exactly the same kind, for example two curve25519- or two ...
2
votes
1answer
60 views

Finding Elliptical curve points and encoding text using them

I recently got into learning Elliptical curve cryptography and are currently building a project in C#. Everything is working well so far, I can encode and decode points, and thanks to this forum I ...
1
vote
1answer
94 views

Elliptical curve cryptography key generation time

I am currently trying to learn more about Elliptical curve crypthography and have finally started to get things working and undestanding the different pieces. I've written a small project in C# and ...
2
votes
1answer
84 views

What is the difference between order of base point and curve order in EC? [duplicate]

When I was read about the elliptic curve cryptography I found some definition about domain parameter of elliptic curve like the follow. But I did not understand something $p$: prime number. $a, b$: ...
0
votes
0answers
40 views

Elliptic curve trapdoor function without modular arithmetic?

From what I understand, an elliptic contains a set points satisfying the equation $y^2=x^3 + ax + b$ together with the point at infity. It seems clear how multiplication with a scalar and a point ...
0
votes
0answers
47 views

How many characters per block in an El Gamal ECC cryptosystem?

While I look for how many characters that can be encrypted using the The elliptic curve ElGamal cryptosystem. of each block found for these lines. But I can not understand Actually in our case we ...
2
votes
1answer
80 views

How many of primitive point on the elliptic curve?

In elliptic curves for cryptography, I know $nG=O$, where $G$ is a base point represented by $G=(x_g,y_g)\ on\ E(F_P)$, where $n$ is Order of point $G$. For example, $P(0,6)$ is a primitive point on ...
2
votes
2answers
101 views

What is primary security in ECC?

I read the following paragraph in a book about Elliptic Curve Cryptography, but didn't understand it: The primary security in ECC is the parameter $n$; where $n$ is Order of point $G$, that is $n$ ...
2
votes
0answers
137 views

As a cryptographer, what are the things I should care about in my implementation of pairing functions?

As a beginner in cryptography, I do not know anything about different pairing types more than their names. So far, I know these names: Ate pairing, tate pairing, eta pairing, and r-ate pairing. I am ...
1
vote
0answers
93 views

How represent message in Menezes–Vanstone elliptic curve cryptography

I ask about represent message in Menezes–Vanstone elliptic curve cryptography I now encrypt function as follow $C_1 = (M_1 * K_1) mod\ P$ $C_2=(M2 * k_2) mod\ P$ My question is about how much the ...
1
vote
0answers
41 views

DLOG in $\mathbb{F}_{p^n}^*$?

Assume that we are given an element $g\in \mathbb{F}_{p^n}^*$ and $g$ does not belong to any of the smaller subfields contained in $\mathbb{F}_{p^n}$. If the degree of $g$ is some number $q$, how much ...
2
votes
1answer
126 views

What are these twist attacks with cost $2^{58.4}$ on NIST P-224 curve, and when do they apply?

This page on Twist security mentions a combined attack and a twist rho attack, applicable in particular to NIST P-224 curve with cost $2^{58.4}$ something, with no mention precise definition of ...
4
votes
1answer
118 views

Understanding Twist Security with respect to short Weierstrass curves

I'm trying to understand the "Invalid-curve attacks against ladders" section of SafeCurves Twist Security page and I have difficulties to apply it to short Weierstrass curves. That section claims ...
0
votes
0answers
24 views

Elliptic Curves Readdition

I found the term re-addition in https://www.hyperelliptic.org/EFD/g1p/auto-shortw-projective.html and I cannot figure out what it is. It has actually same complexity of addition and I dont see the ...
1
vote
1answer
161 views

Why does openssl use SHA1 in ECC when I use secp384r1 curve

I need a small clarification that why openssl using SHA1 in ECC when I am using secp384r1 curve, but in rfc they are saying we should use SHA2. Thing here is am using nanoECC in my DTLS, nanoECC ...
1
vote
1answer
85 views

What can be learned from the ciphertext of LibSodium's crypto_box_detached()?

LibSodium, (https://github.com/jedisct1/libsodium), has a function crypto_box_detached() which does authenticated encryption using the public key of the recipient ...
1
vote
1answer
89 views

Protection of Elliptic Curve Implementations against side-channel attacks [closed]

Recent fast elliptic curve implementations, for example a presentation at Eurocrypt 2014 (earlier presentation slides, the paper) talks about protection against only timing attacks. Why only timing ...
0
votes
0answers
63 views

initiate the elliptic curve

when we consider a curve in a prime field for example Weierstrass form and want to initiate it in Miracl,we should give these inputs for initiate curve: ebrick_init(&binst,x,y,a,b,n,window,nb) ...
0
votes
3answers
121 views

Elliptic curve parameters

What's the meaning of 160 bit Curve in Elliptic curve ? or 192 or 224 or 256 and etc. And What is the standard for selecting this number of bit ? why they don't say 100 bit curve?
1
vote
1answer
77 views

How can convert affine to Jacobian coordinates?

I have a point in affine coordinates: $(x,y)$. What should I do when I want to convert to $(X,Y,Z)$ in Jacobian coordinates? I need it for calculating ECC in a prime field.
0
votes
0answers
69 views

advantages of hashing over elliptic curve signatures for a proof of work protocol

I'm trying to create a proof-of-work protocol for a proof-of-concept software, and it's basically something like this: ...
1
vote
0answers
73 views

Which mathematical operations does secp256k1 point multiplication use?

To convert a bitcoin private key to a public key, the secp256k1 point multiplication math is used. Could I – theoretically – convert a private key to a public key just using the four arithmetic ...
2
votes
1answer
124 views

What is the difference between “secp…” and “sect…”?

The National Institute of Standards and Technology (NIST) recommended elliptic curve domain parameters to have names such as “secp…” and “sect…”. For example: “secp224k1” and “sect571k1”. What is ...
3
votes
3answers
151 views

Why are we not using multiple ciphers per message?

I am aware of at least rsa, elgamal-encryption, and variations of elliptic-curves relying on different problems and that those problems are considered hard. However, if someone figures out a way to ...
1
vote
0answers
86 views

What is the (uncompressed) x,y-representation of a curve point on the P-256 NIST elliptic curve?

I am trying to understand the FIDO U2F Raw Message Format, especially the format in which a user public key should be provided. The documentation says the following: A user public key [65 bytes]. ...
0
votes
1answer
58 views

Is elliptic curve point multiplication semantically secure?

Is elliptic curve point multiplication semantically secure? I'd like to know if there are some sets of elliptic curve parameters (e.g. NIST curves) that are proved to be semantically secure or that ...
-1
votes
1answer
120 views

Bouncy Castle elliptic curve from explicit parameters (E-521)

I'd like to use a curve that's not included in the Bouncy Castle EC named curves spec, specifically E-521. According to the BC javadocs, you need a few values in order to do this: q, a, and b for the ...
0
votes
1answer
55 views

How can i calculate prime of Elliptic Curve?

In many articles i have found directly the calculation of prime elliptic curve. How can i calculate this prime $p$ ? For example if I consider NIST P-256, $ p = 2^{256}-2^{224}+2^{192}+2^{96}-1$. Why ...
2
votes
1answer
204 views

Why is 224 bit ecdsa faster than 192 bit ecdsa?

I ran several benchmarks using openssl on 2 different computers and I got a surprising result. for the Nist 192 bit curve the benchmark result is ...
0
votes
0answers
56 views

Scalar multiplication of elliptic curve point by a fraction

I'm implementing an algorithm that works on a generic finite cyclic group written in the classic multiplicative notation: (G,*) = < g > , n = |g| At a ...
0
votes
1answer
69 views

How to calculate kinv from the given k value

I am implementing an ECDSA NIST test vectors verification application. The test vectors are taken from http://csrc.nist.gov/groups/STM/cavp/#09. One of the test vectors is given below: ...
0
votes
0answers
43 views

Selecting a Bouncy Castle named curve for ECC [duplicate]

I have been tasked with implementing ECDSA and ECDH in Java using the Bouncy Castle library. However, I am unsure of what curve to use. I am aware of the named curves listed in BC, and I've done a ...