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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Can we use elliptic curve cryptography in wireless sensors?

Can we use elliptic curve cryptography in wireless sensors? If so, how do you map points to message characters?
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672 views

ECC algorithm pollard's $\rho$ complexity

One of the methods to break a ECDLP is Pollard's rho algorithm. When ECDLP is defined over a finite field $F_p$, and given a relation $S=w.T$, where S and T are a member of $F_p$. Then ECDLP is to ...
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Is the Representation Problem hard on elliptic curves?

The RP in ECC would be to find $a_1,\ldots,a_n$ (integers) given $P$ and $Q_1,\ldots,Q_n$ (points in the EC) such that $P = a_1 \cdot Q_1 + \ldots + a_n \cdot Q_n$. Is it hard when DH-like ...
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1answer
611 views

Standardized parameters for elliptic curve cryptography

When an elliptic curve-based cryptosystem is deployed, a single set of public parameters (consisting of a particular elliptic curve over a finite field as well as a generator of a prime order subgroup ...
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How does the MOV attack work?

What exactly is the MOV attack, how does it actually work, and what is it used for? It's explained briefly here and I'd like to know what it is more / what is it fully used for.
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Pairing-friendly curves in small characteristic fields

There are several well-known techniques to generate pairing-friendly curves of degrees 1 to 36 on prime fields GF(p): Cocks-Pinch, MNT, Brezing-Weng, and several others. In extension fields GF(p^n), ...
8
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1answer
517 views

Compressing EC private keys

For reasonable security, EC private keys are typically 256-bits. Shorter EC private keys are not sufficiently secure. However, shorter symmetric keys (128-bits, for example) are comparably secure. I ...
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1answer
726 views

Mapping points between elliptic curves and the integers

My primary question is: Is there an easy way to create a bijective mapping from points on an elliptic curve E (over a finite field) to the integers (desirably to $\mathbb{Z}^*_q$ where $q$ is the ...
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2answers
333 views

An Elliptic curve cryptography implementation which can be terminated

I'd like to have an implementation of elliptic curve cryptography along the lines of secp256k1 which is secure until some information is published after which it is broken. One idea would be to use ...
5
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1answer
235 views

How can I use Weierstrass curve operations with a=-3 for implementing operations for a=0?

I am working with golang's elliptic library. It implements functions on Weierstrass elliptic curves with $a=-3$. I need to make my own library that allows me to handle curves with $a=0$. I understand ...
2
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1answer
273 views

Are there reference implementations of ECQV implicit certificates?

I am interested in exploring ECC implicit certificates, specifically using the ECQV protocol. While the actual implementation would not difficult to perform using building blocks provided by most ECC ...
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Basic explanation of Elliptic Curve Cryptography?

I have been studying Elliptic Curve Cryptography as part of a course based on the book Cryptography and Network Security. The text for provides an excellent theoretical definition of the algorithm but ...