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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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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51 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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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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71 views

What is more efficient, pairing based cryptography or non pairing based cryptography? [closed]

As far as I know non pairing pairing based cryptography is less time consuming than pairing based because, pairing based uses complex operations. Are there any advantages of pairing based cryptography ...
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47 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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102 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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118 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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85 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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393 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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116 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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248 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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50 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
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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24 views

Pairing on BN curves, GMP code

Is it possible to write a small implementation of tate pairing using BN curves using GMP. It does not need to be efficient. I just want to understand the steps. Thank you.
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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
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
93 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
102 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
28 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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209 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 ...