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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Why would anyone use an elliptic curve with a cofactor > 1?

In cryptography, an elliptic curve is a group based on a finite field $GF(p^k)$; this group has $n$ elements on it, and we work on a prime-sized subgroup of size $q$. We denote the value $h = n/q$ as ...
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1answer
150 views

How does DJB's nistp224 manage to fit compressed points into 224 bits?

DJB's nistp224 program purports to be an implementation of elliptic curve Diffie-Hellman relative to the standard NIST P-224 elliptic curve. To the best of my ...
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1answer
283 views

How to properly add ECDSA private keys?

I'm currently working on an application that requires me to add two ECDSA private keys in order to make a new private key. The result has to have the property, that its corresponding public key is the ...
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1answer
168 views

ECDSA - point order criterion

i am creating some primitive demostration for ECDSA over small curve (p < 229). But my implementation have some weird issues. Verify process return false even if the signature is correct. Because I ...
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1answer
365 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 ...
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1answer
523 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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1answer
4k views

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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0answers
626 views

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
983 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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1answer
853 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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0answers
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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
554 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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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
533 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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1answer
1k views

What are the advantages of a static ECDH key?

What are the advantages of using "static-ephemeral ECDH" over "ephemeral-ephemeral ECDH"?
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2answers
853 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
254 views

Can you help me understand ECC Cryptography and it's algorithm?

I want to know the basic understanding of ECC algorithm for cryptography. But I am not aware of the algorithm. Can anyone provide me with a basic explanation of the algorithm?
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1answer
450 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
432 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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3answers
35k views

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
317 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
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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 ...
5
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1answer
219 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
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Are there any Secp256k1 ECDSA test examples available?

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
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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 ...
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2answers
384 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
216 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
223 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
624 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 ...
6
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1answer
176 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 ...
10
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3answers
908 views

Are any of the major asymmetric ciphers distinguishable (EG, RSA, ECC)?

Related to "Is it possible to derive the encryption method from encrypted text?". Given ciphertexts generated by any of the major asymmetric ciphers (RSA, ElGamal, ECC, etc..) can these ciphertexts ...
17
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5answers
3k views

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 ...