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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Is there a way to do single key-pair asymmetric encryption?

All of the information on asymmetric encryption I can find uses key-exchanging to get a mutual symmetric key. What I am trying to do is encrypt a message with a public key and have it only readable ...
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0answers
39 views

How to find the integer multiplicand from given two points?

I have two points on an elliptic curve $P(x_1,y_1)$ and $Q(x_2,y_2)$ and a scalar value $x$, where $P=x \cdot Q$. What is the best way that I could figure out the value of $x$? Given that I know all ...
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40 views

Is this ECC based messaging method secure?

I developing an encrypted messaging for ZeroNet (aP2P file-based network, website: zeronet.io) and would like to have some guidelines if any of this could work. My first idea: In ZeroNet every user ...
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0answers
17 views

Strength of a cryptography algorithm [duplicate]

I'm just read this article from Atmel corporation in comparing RSA with ECC cryptography algorithms. First of all please read these two paragraphs quoted from the article: P1: Strength of an ...
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1answer
80 views

Where can I get the correct and precise algorithms for elliptic curve cryptography?

I have been asked to implement cryptographic operations using elliptic curves. I would like to get precise algorithms for various processes like key generation, digital signature and verification. I ...
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1answer
100 views

About end to end algorithm SMS from Jo Mehmet Sollihagen Øztarman [closed]

This is a signcryption scheme from End-to-End Data Protection of SMS Messages by Jo Mehmet Sollihagen Øztarman (pdf, section 4.3.1): Public parameters C: an elliptic curve over GF(ph) with p ≥ 2^...
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0answers
66 views

EdDSA Verification vs. Cofactorless Verification

In the EdDSA for more curve paper the authors defines: Keys An EdDSA secret key is a $b$-bit string $k$. The hash $H(k) = (h_0, h_1, ... , h_{2b−1})$ determines an integer $s = 2^n+\sum_{c≤i<n}...
2
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1answer
54 views

Are private and public key sizes of Elliptic curve related?

I'm new to elliptic curve cryptography. I just want to know in the case where I take a random number (private key) and find its associated public key, does the size of the public key depends upon ...
3
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1answer
110 views

A (current or soon-to-be) NIST-recommended alternative to ECC?

So this comes from the professional rumor-mill, and I'm wondering if anyone might either debunk or shed light on this. My understanding is ECC is generally now preferred over RSA simply due to how ...
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0answers
39 views

ECDH security when no KDF is used

Let's suppose our device performs ECDH with a fixed, unknown, private key $prv$. It accepts as input any point $Q$ lying in the proper subgroup of the proper ellipict curve, then computes: $P = prv*Q$...
2
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1answer
42 views

Is there a single-use signature scheme, where a second use of the private key discloses it to the world?

With ECDSA (and possibly DSA too) I'm aware that if the same value for $k$ is used with the same private key $D_A$ to sign two different messages, then anyone possessing the two messages $m_0$ and $...
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2answers
42 views

With EC secp256k1 is there a way of transforming a function of the private key to a function of the public key?

A key pair has a private key $D_A$ and a public key $Q_A$. $D_A$ is an integer less than the curve's $n$. Is there any (boolean) function of the private key $f(D_A)$ which can be transformed into a ...
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1answer
146 views

With ECDSA is there a way for the verifier to calculate any properties of $k$?

With ECDSA, given $(r,s)$ and $m$, is there a way for a verifier to calculate any (boolean) properties of $k$, without knowing $k$ or the private key $D_A$? (I understand that $k$ should be random, ...
3
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2answers
59 views

How does the size of the prime affect Elliptic Curve Bit Security?

I am using the MIRACL Library to implement an Elliptic Curve Diffie Hellman based Key Exchange according to ECDH-Scheme-Wikipedia. Referring to the Miracl Docs they suggest a few curves. Each curve ...
5
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0answers
41 views

Is it possible and safe to use SAKKE for signing/verification, rather than for encryption?

Is it safe to use the Sakai–Kasahara key encryption algorithm (SAKKE) for signing/verification, rather than for encryption? (Example at bitbucket.org) In particular, I want many Bobs to be able to ...
3
votes
2answers
406 views

Are all possible EC private keys valid?

I usually generate a key pair using openssl or Bouncy Castle. I'm using curve secp256k1. The 256bit private keys look fairly random. Do all values of "private ...
3
votes
1answer
332 views

Do Weak Elliptic Curves Exist?

I'm running into very contradictory opinions when try to understand if weak elliptic curves exist. I'm not interested in the case when a curve's weakness is attributed to properties of an EC's prime, ...
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1answer
72 views

Is it safe to generate ECDSA keys from the hash of the previous, over and over again?

I have memorized a very long and secure passphrase, that when hashed with sha256, I can use the result as an ECDSA private key, and use it as a brain-address for Bitcoin. Now I need more bitcoin ...
5
votes
1answer
115 views

Why not to use curve over field of $p^m$ with $p > 2$ for ECDSA?

I'm reading the ECDSA paper and they say you can only use ECDSA with odd-power fields $p$ or with binary fields $2^m$. Why not other power prime fields?
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1answer
39 views

How to use a secret to allow the generation of public keys, where the private keys can be calculated later

Alice has a secret S and publishes some public information P, about S which is insufficient ...
4
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3answers
151 views

Safe curves in Weierstrass form?

I would like to implement a protocol using elliptic curves. I'm thinking of using MIRACL so using curves in their Weierstrass form is preferable as it they are supported by this framework. I don't ...
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0answers
35 views

ECSchnorr Still getting wrong (hash?) results [closed]

I'm writing Schnorr signature algorithm on elliptic curves. I get instructions from here (page 128) Here's my code ...
4
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2answers
174 views

Curve25519 - Alice can decrypt her own message to Bob?

I'm developing an application with multiple clients and one server. All clients will have the same hard-coded Curve25519 key pair as well as the server's public key. The server will have its own key ...
2
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1answer
110 views

Can j-invariants be used to decide which elliptic curves are suiteable for cryptography?

The j-invariants classify the elliptic curves up to isomorphisms (if we suppose to work in the algebraic closure). Is this classification used in some way to decide whether or not an elliptic curve ...
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2answers
137 views

How do you derive the lambda and beta values for endomorphism on the secp256k1 curve?

Note: This question was reposted from Bitcoin Stack Exchange, where it received alike answers. You can see a little background about this on this bitcointalk post by the late Hal Finney. $\beta$ ...
4
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1answer
99 views

Are EC public/private keys significantly weakened by having a known byte?

I would like to use different EC keys for different purposes in an app, and I would like to easily see the purpose for which particular key (pair) was generated. With ~65K attempts, I can generate a ...
2
votes
1answer
71 views

Multiplication in elliptical curve cryptography

I'm practising for a cryptography test and came across this question: Let us assume that for a specific elliptic curve the formulas for the computation of $(x_3, y_3)=R+S$ are given by: $X_3=...
3
votes
1answer
55 views

How to compromise the privacy of NaCl encrypted messages, when nonce is reused?

I want to know to how break NaCl encryption when a nonce used more than once for a given key private key. According to PyNaCl docs: It is VITALLY important that the nonce is a nonce, i.e. it is a ...
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0answers
13 views

Transforming EC public key X and Y-sign into X and Y [duplicate]

I'm using bouncycastle which uses X and Y coordinates for public keys. An EC public key is more compactly represented by the X coordinate and the sign of the Y coordinate. How do I use bouncycastle ...
6
votes
2answers
299 views

How does Diffie–Hellman differ from elliptic curve Diffie–Hellman?

I didn't understand how ECDH actually works. Disclaimer: I know very little about elliptic curves. Here is how DH works: Alice and Bob agree on a prime number $P$ and a generator $G$. (They use one ...
3
votes
1answer
105 views

Can a billion elliptic curve keys be generated on a laptop in less than an hour?

I want my application to generate an EC key pair. The first four bytes of the sha256 hash of the public key should contain a known IP address. As hashes are one-way functions, I need to brute force ...
2
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1answer
268 views

ECDH or RSA more secure for symmetric key wrapping?

Suppose a message is encrypted with a symmetric block cipher with a random key. RSA is often used to wrap the symmetric key using the recipient's public key. In this case, the size of the message is ...
2
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0answers
56 views

Using a product of a series of curve25519 scalars as a private key

There are a few systems like the GNU Name System and the Sphinx mixnet packet format that employ a series of curve25519 scalars all multiplied together as a private key. Are there any caveats to ...
2
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0answers
50 views

Construct points with the same discrete logarithm

Assume we have an elliptic curve $E$ with a Tate (or Ate,...) pairing $G_1 \times G_2 \mapsto G_T$ Now the task is to find $g_1, g_1' \in G_1$ and $g_2, g_2' \in G_2$ such that the discrete logarithm $...
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4answers
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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 ...
4
votes
3answers
141 views

Calculating $\mathbb F_{p^2}$-rational points of an elliptic curve defined over $\mathbb F_p$

How can I calculate points on an elliptic curve defined over $\mathbb F_p$, for example $y^2 \equiv x^3 + 1 \pmod p$, with coordinates in $\mathbb F_{p^2}$? (points might have complex number format in ...
6
votes
1answer
108 views

How to exctract ECDH parameters from an OpenSSL-generated $G$?

I'm using ECDH for generating ECDH public parameters (p,a,b,G,n), I try to get this values using openssl ecparam -in cert.pem -text -noout For ...
7
votes
1answer
186 views

How can ECDSA signatures be shortened (to be used as a product key)?

So I made my own serial key generation software, using ECDSA, for use in my own applications and it works great so far! To keep the serial key short enough I use a 128 bit EC curve. My final signature ...
5
votes
2answers
665 views

Safe elliptic curve point addition using projective coordinates: How do I tell if the points are the same?

I am trying to implement elliptic curve point addition in hardware for NIST p256 and p384 curves. I have noticed the following issue with the suggested NIST routines: Consider routine 2.2.7 of http://...
3
votes
1answer
104 views

Do ECDH and ECDSA combined solution provide an authenticated protocol exchange solution in MCU environment?

I'm working on a project in MCU (micro controller) environment with GPRS connection to exchange data securely with the cloud. The encryption algorithm has been selected to use AES. I did some search ...
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2answers
694 views

Reuse of a DH / ECDH public key

I was wondering whether it is safe to use the same DH or ECDH key pair in more than one key agreement, particularly if these public keys are in a public registry. These public keys could be used by ...
5
votes
0answers
67 views

Elliptic curve point addition with $Z_1 = Z_2 = 1$

Elliptic curve point addition and point doubling operations using Projective and Jacobian coordinates require fewer field multiplication operations when considering $Z$ coordinates of input points ...
4
votes
1answer
198 views

Why a key pair is used in OpenSSL ECDSA_sign or ECDSA_do_sign instead of only private key ?

If the digital signature in ECC (ECDSA) is made using a private key, why is the OpenSSL library using ECKEY pair as an input parameter instead of the private key only ?
2
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1answer
343 views

Forward-secure static-ephemeral ECDH key agreement protocol

The question is whether the following simple key agreement protocol design has good security properties, and how it can or should be improved. Assumptions Alice is a persistent entity with a static ...
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32 views

Where can I find a versatile PKI and library leveraging curve25519?

I note that Things that use Curve25519 provides a long list of protocols, software, and libraries that leverage curve25519, but I'm wondering if there is any such software that more fully implements a ...
11
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1answer
607 views

How to calculate elliptic curve parameters?

I'm having a rough time understanding the math behind elliptic curves. I want to implement ECDH where user can define a, b, and p parameters of elliptic curve. How can I calculate generator base ...
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0answers
48 views

What is the hardness in Decisional Linear Assumption (DLIN)?

I had understood what does the DLIN assumption means and here is a related question. But I fail to understand the 'real hardness' in this problem. I would be grateful if someone can help me to ...
4
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1answer
143 views

ECDH and ECDSA in PGP with known public key

How are used ECDH and ECDSA in combination with public key ? Usually these methods are used for establish a secret themselves, ...
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1answer
111 views

OpenPGP Public-Key algorithm

What means when pgpdump shows this kind of algorithm in the Public-Key Encrypted Session Key Packet? ...
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2answers
311 views

How to derive a symmetric key from ECDH shared secret?

I am trying to implement the internal primitives of ECDH. Currently I'm able to multiply the receiver's public EC point with the sender's private key to arrive at the shared EC point. Next step is to ...