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.

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Is this EdDSA modification secure?

I am hoping to employ a signed set membership system which is valid iff each signer's contribution to the set is present. The system should allow for two or more mutually exclusive signed sets to be ...
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101 views

Is an elliptic curve over $\mathbb{F}_p$ order preserving for the points $(x,y) \in \mathbb{Z}_p$?

Let $E\colon y^2=x^3+ax+b$ be an elliptic curve, and consider its realisation over the finite field of prime order $p$: $E(\mathbb{F}_{p})$. Then if $0<a,b$ is the following true? $$\forall ...
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327 views

openSSL ECDH private key size

When you are using a named curve like P-256 in openSSL, is there any standard key size for ECDH private key keys? If you look at the ec_key.c file in the openSSL ...
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1answer
304 views

Key space: Dense and sparse

I'm taking a cryptography class and I come across these terms dense and sparse key space allt he time. What do they mean? As far as I can I understand, dense key space means that there are more ...
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274 views

Can you help me understand ECC Cryptography and it's algorithm?

I want to know the basic understanding of ECC algorithm for cryptography. But I am not aware of the algorithm. Can anyone provide me with a basic explanation of the algorithm?
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59 views

Is there any patent free EC point compression available? If not, should I GPL/LGPL my code?

I'm currently using the BouncyCastle implementation in uncompressed mode, and considering releasing an optimized version of EC code that uses point compression. It appears the only thing limiting me ...
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48 views

How do you derive the lambda and beta values for endomorphism on the secp256k1 curve?

You can see a little background about this on this bitcointalk post by the late Hal Finney. $\beta$ and $\lambda$ are the values on the secp256k1 curve such that: $$\begin{align} \lambda^3 &= 1 ...
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108 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.
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84 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 ...
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58 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 ...
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192 views

ECDSA - point order criterion

i am creating some primitive demostration for ECDSA over small curve (p < 229). But my implementation have some weird issues. Verify process return false even if the signature is correct. Because I ...
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6 views

Curve41417 example

I have done an example, attached as image file, of the algorithm in Curve41417 by Daniel J. Bernstein et al. but my answer is not correct. I have checked it multiple times but couldn't find the ...
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20 views

Is it possible to encrypt x coordinate of an EC point with a password? [on hold]

With reference to EC based password authenticated key exchange protocol I have a question: What are the problems arise if x coordinate of an EC point is encrypted using a pre-shared key like ...
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22 views

RSA_DH vs ECDH implementation

In ECDH protocol is possible, naturally, to use the same algorithm for calculate a secret key for both communication parties (Alice and Bob for example). It is possible to design also a same algorithm ...
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32 views

Encryption on mobile devices? [closed]

I have studied the basics of cryptography, so it would be okay to say that I am familiar with the concepts of Cryptography (Theoretical). I have surfed the net for days to implement my theoretical ...
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28 views

Generating interactive, secure multiple ECC key pairs deterministically

In Elliptic Curve Cryptography (ECC) assuming user A has a private public key pair of $S$, $P$ accordingly with generator point $G$ which as we know is: $$P=S*G$$ Assuming that user A wants to ...
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28 views

EC based password authenticated key exchange protocol

I would like to know: What is the currently best (efficiency and security wise) known EC based password authenticated key exchange protocol? (i.e. is there any EC based protocol may be similar to DH ...
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57 views

Popularity of ECMQV authenticated key agreement protocol

I've got a few ECMQV related questions: Why is ECMQV a more efficient EC-based authenticated key agreement protocol? Why is ECMQV so popular? Is it because no other protocol of its strength exists? ...
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67 views

Is there any pattern in points on EC?

I read some where in crypto.stackexchange answer (related to EC-SRP protocol) that there is pattern in points on elliptic curves, i.e. if given some points containing mix of correct and wrong points ...
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62 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 ...
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76 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 ...
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67 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 ...
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86 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.
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37 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 ...
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49 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 ...
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27 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 ...
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68 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) ...
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72 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: ...
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1answer
204 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 ...
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65 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 ...
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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 ...
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39 views

Size of Messages Exchanged by PRV and VER for Schnorr Protocol

In this file Elliptic Curve Based Zero Knowledge Proofs and Their Applicability on Resource Constrained Devices I don't understand the Table 6 (Table 6: Size of Messages Exchanged by the Prover(PRV) ...
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148 views

RSA and ECDSA Certificate Sizes

Is there a table (or a whitepaper from official sources) that compares the size of X509 certificates generated with RSA (starting from 1024 bits) and ECDSA (starting from 160 bits) ? Thanks for the ...
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104 views

becoming a cryptographer after math studies [duplicate]

After studying philosophy and being a philosophy teacher, I took back studies 4 years ago and I did a bachelor in maths. I'm in maths grad school now (I'm 32), and I would like to work in ...
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2answers
48 views

Elliptic Curve Cryptography Encrytion and text representation implementation

I'm writing a coursework and right now I've implemented the ECDSA algorithm, but I also need to encrypt and decrypt small text files (.txt) using elliptic curve cryptography. The problem is that I do ...
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2answers
399 views

Reuse of a DH / ECDH public key

I was wondering whether it is safe to use the same DH or ECDH key pair in more than one key agreement, particularly if these public keys are in a public registry. These public keys could be used by ...
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72 views

Is size Q equal to size SHA(Q)? [closed]

Assume d is a 128 bit random integer and P is base point of an elliptic curve and Q = dP is a point on the elliptic curve and SHA is a hash function with 128 bit output, my question is: Is size Q ...
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1answer
95 views

Integers in ECC

Let A be a point on curve with integral coordinates. Does k.A necessarily have integer coordinates? If so than why and if not than how to find A and k such that k.A has integral coordinates.
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1answer
84 views

How Proof all Subgroup point of prime order elliptic curve have prime order [#G=#E]? [closed]

anyone knows any reference that proof it ? Please Help .
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1answer
89 views

counting points not on elliptic curve [closed]

Given an curve with equation $y^2=x^3+ax+b$, I want to find the number of pairs $(a,b)\in \mathbb{F}_p \times \mathbb{F_p}$ NOT on the curve. How do I do it? I have an intuition that it is $p$, but ...
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0answers
16 views

How to get the (x,y) from the EC point in the pubkey of an ECDSA certificate?

I have this certificate, and I have the bitstring of the pubkey that should represent Q = (x,y) = [d]P. How can I get the x part? (The curve is the NIST B-163)
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2answers
165 views

pairing-based schemes

some authors claimed that computational performance of a pairing-fee scheme (based on scalar multiplication over an elliptic curve group) is about 1000% more efficient than a pairing based one I would ...