# Tagged Questions

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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### Bilinear pairing

I am working on Efficient Construction of Pairings which are being realized by Miller's algorithm. In this algorithm the basic steps are point doubling and line function computation point addition ...
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### Encryption time in ECC

In RSA, encryption time is usually much less than decryption time due to having a small public exponent. Can this be achieved in Elliptic Curve Crypto (ECC)?
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### 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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### How to handle the GCD(V,P) != 1 case when doing point addition or point doubling in elliptic curve cryptography

The equation for a finite field Elliptic Curve is of this form: $$y^2 \equiv x^3 + a * x + b \pmod{P}$$ When we do common EC operations like point doubling or point addition we need to calculate the ...
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### Want to use ECC but am clueless [closed]

First off, I'm not an experienced cryptography or computer person, please bear with me. I have some basic experiences with PGP software though (not much of a redemption huh?). I have some data that I'...
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### order of elliptic curve divisible by prime

Why order "u" of an elliptic curve "E" defined over a finite field "GF (q)" (u = | E / GF (q) |) must be divisible by a large prime number r to be appropriate for cryptographic purposes?
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### Is C25519/Ed25519 “twist secure”?

This recent new curve mentions something that's new to me: twist security. http://safecurves.cr.yp.to/bada55.html Are the existing C25519/Ed25519 curves secure against this form of attack?
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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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### ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
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### ECC partially blind signature scheme verification

Continued from Is there a flaw in this ECC blind signature scheme? The problem I needed a partially blind signature scheme for one of my projects, but couldn't find one on the internet, so I've made ...
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### Is there a flaw in this ECC blind signature scheme?

Recently I've found the following work on the internet: An ECC-Based Blind Signature Scheme The paper claims to be an ECDSA blind signature however it seems that their scheme has a flaw in it. The ...
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### Security benefits of Ed25519 generating signatures deterministically

I am reading on the Ed25519 curve, and I am trying to understand a claim. Here is the claim: Foolproof session keys. Signatures are generated deterministically; key generation consumes new ...
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### Smart card Strong authentication / Verification ( fingerprints)

I'm trying to make a strong authentication software and embedded software in a java card. I have found many papers and publications about the subject… too much information to process and I'm working ...
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### ECC public key encryption and authentication - ECIES with ECDSA vs ECDH with AES

I'm currently working on a project where I want to establish a secure and authenticated communication channel between to entities, using Elliptic Curve Cryptography. Now I'm not really sure how to ...
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### Is pairing based cryptography ready for productive use?

I'm currently testing one among those many interesting cryptographic protocols based on bilinear maps. It's quite hard to understand the underlying fundamentals, especially since there are several ...
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### Why does knowing the number of points on a curve help solve ECCDLP?

Perhaps, this is a really obvious question, but I am still having trouble understanding how this all fits together. Why is knowing the number of points on an Elliptic Curve helpful in cracking it? ...
520 views

### ECC Complexity order of point addition, scalar point multiplication and selecting random point

I am facing this problem in calculating the order of a process which involves ECC point addition: $P+Q$ , scalar multiplication: $aP$, and selecting random points in the group. The group is of prime ...
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### Finding an x such that xP = (11,44) on an elliptic curve

Given the elliptic curve $$E:y^2 = x^3+17x+5 \mod 59$$ with point $P = (4,14)$, how do I find $x$ such that compute $x\cdot P = (11,44)$ Is there a mathematical method to compute $x$, or do I ...
261 views

### 64 bit Elliptic Curve key?

For a simple proof of concept project i'm (attempting!) to do, i've started looking into openSSL elliptic curve cryptography. However instead of the standard key lengths, 160-512. I'm interested in ...
279 views

### Weil pairing implementation - low level programming language

I'm just started to studying elliptic curve cryptosystems. My one month-goal is to write a simple signature system based on the Weil-pairing. Some parts of it can be written without deeper ...
472 views

### Fast modular reduction

I am looking at ways to speed up modular reduction for the polynomial $$2^{256}-2^{32}-2^9-2^8-2^7-2^6-2^4-1$$ I have read the paper "Generalized Mersenne numbers" by J.A. Solinas, but it does not ...
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### Sextic twist of BN pairing parameters vs security

I've previously asked questions on BN pairing parameters. Here's one more. In the BN construction, one is working in a subgroup of a curve over an extension field $\mathbf{F}_{p^{12}}$ for some ...
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### Gallant-Lambert-Vanstone method

I am experimenting with the GLV method but cannot manage to get the right results according to the literature. I managed to find lambda, beta, split $K$ into $k_1$ and $k_2$ etc. for the curve I'm ...
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### Sextic twist optimization of BN pairing - cubic root extraction required?

I found the following paper really interesting: http://www.researchgate.net/publication/220378229_A_family_of_implementation-friendly_BN_elliptic_curves/file/79e4150b3a773beecd.pdf It allows ...
4k views

### Using ECDSA keys for encryption

I know that ECDSA is used for signature only, but I wonder if I can use the public/private Elliptic Curve keys for encryption too. I have ECDSA SSH public keys and I wonder if I can use them to ...
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### Does a cofactor of an elliptic curve have to be an integer?

What are the implications of a curve having a non-integer co-factor for its generator point? Is that even possible?
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### Known vulnerabilities in (EC-)KCDSA

Does anybody know if there's known vulnerabilities in KCDSA/EC-KCDSA? I have been researching for the past few hours and I haven't found anything. Wikipedia has very limited amount of information and ...