Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also ...

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Converting ECC Code from python to Java. Extended Euclidean Algorithm not working. [closed]

I'm in the process of converting a Python program I found for calculating ECDSA public keypairs from a given private key. In this particular case it's on the Bitcoin curve. ...
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1answer
278 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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117 views

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

Looking for the number of characters that can be encrypted using the The elliptic curve ElGamal cryptosystem of each block, I found these lines. But I cannot understand them: Actually in our case ...
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14 views

hash function for elliptic curve co-ordinates

Is there any hash function which takes the co-ordinates of an elliptic curve $E_p(a,b)$ as input and gives an integer value i.e. $h(.) : \{(x,y) \in E_p(a,b)\} \rightarrow \mathbb{Z}$
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36 views

If I encrypt data with two different ECC Private keys, how secure is the result?

I'm wondering whether encrypting data with two different 256-bit ECC keys will result in a more secure encryption (minimum 384 bit equivalent) or will result in data that's effectively encrypted with ...
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43 views

What is proper size of window Using RSA Window method?

I want to Use Window method for RSA modular Exponentiation. because of SCA. But I don`t know what is proper window size.
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31 views

Has anybody implemented BGN cryptosystem to multiply two plain texts?

I have tried to use this code as follows, http://stackoverflow.com/questions/33581962/bgn-implementation-in-java but the issue is, when it generate the pairing, the output is in GTfiniteelement (for ...
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42 views

Weil Pairing - Miller's Algorithm

I'm trying to implement Weil Pairing using Miller's algorithm. I have got couple of questions. How to select $m$? As stated in this link page 13, I interated from $1$ to order of point $P$ such that ...
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56 views

Smart Card choice for PKI implementation

I'm seeking to implement a national digital signature standard on a smart card. I feel like this is a good place to ask if anybody is acquainted with a hardware supplier offering smart cards that ...
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0answers
36 views

How common are non-RSA digital certificates?

Is there a statistic available that shows just how common are DSA or ECC certificates amongst webservers? I know that RSA-based certificates are the most common, however I'd like to know, if there is ...
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1answer
50 views

Proper forward secrecy [closed]

Currently I have a protocol using a simple RSA to AES handshake. I have been reading more and more and would like to implement proper forward secrecy, but at the same time I'd like to improve the ...
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2answers
53 views

How to define order according to domain parameters in elliptic curve pairing groups

According to domain parameters, as an example Type 1 pairing domain parameters are ...
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0answers
53 views

Is there any difference between NIST and SECP curves in-terms of their algorithms and implementation?

I'm implementing ECDSA for NIST P-256 curve. I just want to know the same implementation will work for SECP curves also?. If it doesn't, then please suggest me references of algorithms or sample ...
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48 views

Simulation of a custom build network security algorithm with ElGamal Cryptosystem using Elliptic Curve

I am trying to build an algorithm to encrypt and decrypt text using ElGamal Cryptosystem using Elliptic Curve. My algorithm generation is done. But at simulation part I stuck. My algorithm steps are ...
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25 views

Do most TLS 1.2 implementations express curves in a canonical form when performing EC arithmetic?

Sorry if this is a silly question, but does anyone know if the cryptographic libraries which implement TLS 1.2 for Firefox, Chrome, etc. express a given curve in a canonical form (i.e. one of ...
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1answer
63 views

Comparison Affine Coordinates and Projective Coordinates Addition in Excel

Kurve : EC : $y^2=x^3 + x + 1$ Generator:$(1,7)$ $p=23$ Result in Affine use Excel: $P=(1,7)$, $Q=(7,11) \implies P+Q=(18,20)$ Result in Projective use Excel: $P=(1:7:1), Q=(7:11:1) \implies ...
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72 views

Degrade in performance with SSL_OP_SINGLE_ECDH_USE?

We have used SSL_OP_SINGLE_ECDH_USE when setting up our SSL_CTX . This seems to be causing a degrade in performance. I'm not able to find proper documentation for it except that it generates new ...
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73 views

Semaev summation polynomials

I am little confused how this attack works. We have the points $P, Q$ such that $Q = nP$. We let $u_{1} $and $u_{2}$ such that $R(x,y)=u_{1}P+u_{2}Q$. Then if we find the solution $x_1,...,x_n$ of the ...
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30 views

Using Montgomery ladder to calculate the coordintes

In one of my assignments I need to solve the below: For a Montgomery curve $3v^2 = u^3+u^2+u$ over ${\mathbb{F}}_{11}$ and point $P = (9,8)$. I need to compute $x$ coordinate of $3P$ using ...
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52 views

Translation of Schorr Ring Signature to ECSchnorr Ring Signature

I have to write an EC version of Schnorr Ring Signature Scheme. I've already wrote regular ECSchnorr Signature Scheme using this (page 128). I've found a scheme of Schnorr Ring Signature Scheme (page ...
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32 views

Is it possible to re-generate ECPublic key from raw private key and curve params?

As per my understanding, in Elliptical curve cryptography, the EC PrivateKey is nothing but a bigInteger value. If you know the curve specs and you have this private BigInteger value (which I am ...
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17 views

Strength of a cryptography algorithm [duplicate]

I'm just read this article from Atmel corporation in comparing RSA with ECC cryptography algorithms. First of all please read these two paragraphs quoted from the article: P1: Strength of an ...
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51 views

How to sign an elliptic curve point using an ECC signature scheme?

In Schnorr based ECC signature scheme, a message $M$ is signed with the private key $\mathit{sk}$ as $$s=\mathit{sk}\cdot h(M,R)+k$$ where $R=k\cdot P$ and $P$ is a base point. If $M$ is a point ...
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48 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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105 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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123 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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88 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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1answer
410 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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122 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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0answers
266 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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107 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
54 views

elliptic curve point doubling in Jacobian coordinates

I am writing an application that uses Elliptic curve Diffie–Hellman for authentication. I found two formulas for point doubling in Jacobian coordinates. 1st) \begin{equation} X_1 = (3x^2 + aZ^4)^2 ...
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1answer
49 views

Could someone explain the given algorithm?

The following snapshot of the algorithm is taken from the book Guide to Elliptic Curve Cryptography published by Springer 2004. I don't understand that why at the statement 9.1 if both $T_1$ and ...
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1answer
103 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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1answer
78 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
99 views

About end to end algorithm SMS from Jo Mehmet Sollihagen Øztarman [closed]

This is a signcryption scheme from End-to-End Data Protection of SMS Messages by Jo Mehmet Sollihagen Øztarman (pdf, section 4.3.1): Public parameters C: an elliptic curve over GF(ph) with p ≥ ...
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1answer
21 views

How to find HEXA value of String [closed]

This may be very easy thing, but i am just unable to understand this. I have a string "Hi", and in HEXA its written like this ...
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1answer
102 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
94 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 .
-3
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1answer
29 views

How do we calculate DHKey using A's public key and B's private key?

I have 2 set of public/private keys. I would like to know how I can calculate DHKey. e.g: ...
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2answers
213 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 ...