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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Current mathematics theory used in cryptography/coding theory
What are the mainstream techniques borrowed from algebraic geometry (or some other branch of mathematics) which are currently used in cryptography/coding theory? I've only heard about a small subset ...
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1answer
182 views
ECIES protocol - what does the || operation mean?
I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. A there is a problem I don't understand operation $||$. What this operation mean?
Some stuff is ...
3
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1answer
290 views
Elliptic curves for ECDSA
i'm trying to implement parameters generation for ECDSA according to SEC1 v2.0:
Input: The approximate security level in bits = t is {80, 112, 128, 192, 256}
...
4
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1answer
440 views
advantages of a static ECDH key
What are the advantages of using static-ephemeral ECDH over ephemeral-ephemeral ECDH?
3
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1answer
451 views
X9.62 Multiplying an elliptic curve point by a number
I'm currently trying to implement ecdsa and the first problem i met -- multiply an elliptic curve point by a number.
As far as i understand X9.62 gives some recommendation for doing it but i ...
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2answers
334 views
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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2answers
334 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 ...
5
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1answer
195 views
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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0answers
46 views
Elliptic curve Cryptography [duplicate]
Possible Duplicate:
Can we use elliptic curve cryptography in wireless sensors?
How to map message character to point lies on Elliptic Curve? how to ecc used in wireless sensor networks? ...
4
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1answer
260 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 ...
7
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2answers
407 views
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.
6
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3answers
513 views
Can ECDSA signatures be safely made “deterministic”?
Using the terminology of the ECDSA wikipedia page, ECDSA (and DSA) signatures require a random k value for each signature which ensures that the signature is different each time even if the message ...
6
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2answers
246 views
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), ...
6
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1answer
273 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 ...
2
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1answer
242 views
Families of public/private keys in elliptic curve cryptography
I'm looking for a related key scheme for elliptic curve cryptography. The basic idea would be that there would be a master public key and a master private key. From the master public key, you could ...
2
votes
1answer
366 views
What does SSL use? RSA? El-Gamal? Elliptic curves?
I'm not sure what SSL uses to share the symmetric key to both end users, i.e. at the beginning of the communication. Is it RSA? Or El-Gamal? Or something else?
Thanks!
9
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1answer
397 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 ...
4
votes
2answers
231 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
votes
1answer
132 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 ...
1
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1answer
121 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 ...
6
votes
1answer
521 views
Secp256k1 test examples
Are there any available test cases for testing elliptic curves like secp256k1 (Korblitz curves from http://www.secg.org/collateral/sec2_final.pdf)? For curves like P192 there are for example those ...
12
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4answers
4k views
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 ...
5
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1answer
119 views
Are there security issues with discrete logarithm keys not being uniformly distributed?
Generally, algorithms based on discrete logarithm specify that private keys are chosen as scalars between 1 and the order of the group (denoted q here). For instance IEEE P1363 and FIPS 186-3 both ...
8
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2answers
555 views
Are any of the major asymmetric ciphers distinguishable (EG, RSA, ECC) ?
Related to this question.
Given ciphertexts generated by any of the major asymmetric ciphers (RSA, ElGamal, ECC, etc..) can these ciphertexts be distinguished from random noise? Justify why, why ...
