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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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 ...
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1answer
300 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}
...
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How strong is the ECDSA algorithm?
Some cryptographic algorithms are as strong as the size of their key is, while other have some weaknesses that limit their strength (such as SHA-1). How strong is the ECDSA algorithm, and does that ...
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Elliptic curve cryptography related key attacks
This question is an extension of Families of public/private keys in elliptic curve cryptography
As described above, bitcoin "type 2" deterministic wallets use a root private/public key pair, where ...
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2answers
510 views
Can one reduce the size of ECDSA-like signatures?
Using $n$-bit ECDSA, a signature has a size of $2·n$. It is possible to recover the public key from this signature, which shows that there is a publicly visible redundancy in the signature.
Is ...
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471 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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259 views
Diffie hellman key exchange on elliptic curve over an extension field [closed]
I am attempting to do a final semester project where I implement Diffie-Hellman key exchange on an elliptic curve over an extension field (2^256). Can anybody help me to generate the extension field ...
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2answers
345 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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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? ...
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2answers
357 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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1answer
265 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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457 views
advantages of a static ECDH key
What are the advantages of using static-ephemeral ECDH over ephemeral-ephemeral ECDH?
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419 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.
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1answer
282 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
250 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 ...
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1answer
380 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!
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3answers
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Why is elliptic curve cryptography not widely used, compared to RSA?
I recently ran across elliptic curve crypto-systems:
An Introduction to the Theory of Elliptic Curves (Brown University)
Elliptic Curve Cryptography (Wikipedia)
Performance analysis of identity ...
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2answers
234 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 ...
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3answers
526 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 ...
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1answer
135 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 ...
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1answer
567 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 ...
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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 ...
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2answers
271 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), ...
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1answer
127 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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1answer
197 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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1answer
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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 ...
5
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1answer
128 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 ...
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2answers
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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 ...
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5answers
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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 ...
