Questions tagged [elliptic-curves]

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 consider more specific tags such as discrete-logarithm and ecdsa.

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111 views

Are different elliptic curves compatible?

Regarding SubtleCrypto and curves P-256, P-384 and P-521. Can I mix two different curves for key derivation? For example performing key derivation between P-256 and P-521. EDIT: Can I mix two ...
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99 views

CSIDH Squaring Fixing the Base Curve

Consider the following variants of the CSIDH squaring problem. P1. Given $sE, E$ where $s$ is a random ideal class and $E$ is a random curve (reachable from initial $E_0$), find $s^2E$ P2. Given $sE_0$...
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Problem with the signature of message using ECDSA over GF(2^m)

I'm trying to set up an ECDSA with Elliptic Curves over $\operatorname{GF}(2^m)$ with an example of toy with the following values: Using the Weierstrass equation on binary finite fields. $$E: y^2 + x*...
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Doubt on elliptic curve over a finite field and binary representation

I'm a programmer, i.e. agnostic to the mathemathics behind most of cryptographic scheme, but I'm trying to remediate. I'm writing this premise for any possible error or imprecision that I probably put ...
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125 views

Research Guidance on Elliptic Curve Cryptography [closed]

I am a freshman who want to research elliptic curve cryptography. There are a few questions I have: Firstly, I am not sure about how I should narrow down the topic. Where should I focus on? Can I ...
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35 views

Which signature is considered more secure and has less communication cost?

This article uses Elliptic Curve Cryptography, but when it comes to signing and verifying messages it is not using the ECDSA signature algorithm. In the article, they mentioned that the communication ...
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Is this good way of Elliptical curve point mapping

Mapping a bit string $L$ to elliptical curve point in say prime field $\mathbb Z_p$. A simple way would be to use an integer mapping function that maps $L$ to a number $\{1, q\}$ where $q$ is the ...
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83 views

How does one go about implementing a range proof?

I've attempted to find a solution to this problem, but for the life of me I am unable to. I am attempting to solve whether a point an elliptic curve of prime order is between 2 points, given a ...
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84 views

A card game (for mental poker or any other card game)

I thought of a way to produce trustless card game in a flexible way. One feature that I want is it should be flexible (It should work for any type of card game, though I indeed started it as a ...
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How to construct Hash function in python3? [duplicate]

In many cryptographic protocols design like this one, I have seen the statement 'Choose a Hash function for example: \begin{align} h&: \{0,1\}^*\times\mathbb G\to\mathbb Z_q^*\\ h_2&: \{0,1\}...
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Known attacks against ECC in case many multiples are known?

Suppose there's a secret value x, an elliptic curve with the (public) generator G, and a sequence of secret values ...
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29 views

CMS encryption application using Windows system certificate store

Hy! I'm looking for an application, which can make cms encryption/decryption, but with the use of the windows certificate store. I already found out, that openssl can't do it out of the box (just by ...
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What's going on with the complicated implementations for map_to_curve in draft-irtf-cfrg-hash-to-curve?

I've been looking into implementing cPace, and I saw that two cipher suites defined for it refered to draft-irtf-cfrg-hash-to-curve for its protocol definition. Part of cPace requires mapping a string ...
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Which of these ECC libraries is more secure, fast and commonly used? [closed]

I have a python project and for this project, I need to use Weierstrass-based ECDSA. On the web, I've found two libraries; Library 1 is called fastecdsa: Library 2 is called ECPy: I couldn't see any ...
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124 views

Breaking Elgamal private key

I have been given a task to explain if - given a public key and a portion of a private key (over 300bits) with a remain unknown of 80 bits - the private key can be broken with an algorithm faster than ...
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160 views

Break El Gamal for Elliptic Curves

There is an elliptic curve El Gamal digital signature scheme. Alice fixes an elliptic curve $E$, a prime $p$, a point $A$ on $E$, a secret integer $a$, and computes $B = aA$. She makes $(E, ...
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451 views

Why do the discriminant and primality of the group order of an elliptic curve affect security?

In a book about cryptography and elliptic curves, there was a mention that not all curves are secure, and a statement than in order to pick a secure curve the curve must satisfy 3 requirements. The ...
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1answer
125 views

Which crytographic libraries to use for Elliptic Curve Cryptography and Bilinear Pairing?

I'm currently trying to implement a solution for Vehicular ad hoc networks based on cryptography. I choose to use python to implement the solution, but I don't know which libraries I have to use to ...
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238 views

Finding scalar that creates a point with zero X-coordinate for popular elliptic curves

In signature creation in ECDSA we use a nonce, commonly identified as $k$. To create an ECDSA signature, we need to calculate two integers, commonly identified as $r$ and $s$. $r$ is simply the X-...
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106 views

ECDH - when are the domain parameters shared and how?

I'm trying to understand Diffie–Hellman based on Elliptic-curves. Can one explain at which point of time the domain parameters are shared? Are they shared trough a public channel and can they be ...
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1answer
99 views

Why is a random component needed for ECDH key pair generation in Mbed TLS?

Please forgive me if this is not the right place, however, I encountered this TLS implementation with a function that generates an ECDH key pair on an elliptic curve: In addition to the private key ...
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82 views

Is this a good implementation of digital signature with timestamp?

Is this a good practice ?. How good or bad is this compared to appending a timestamp to the actual data and hashing it as represented below. ...
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885 views

What is a "constant time" work around when dealing with the point at infinity for prime curves?

I've been working for some time, on designing a constant time solution for dealing with the "point at infinity" for prime curves. So, far I'm using the Standard Projective Coordinates for ...
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2answers
362 views

How to find the base point given public and private key and EC parameters except the base point

I'm working on the curve secp256k1 and I've private key $k$ and public key $P = [k]G$. I look for solutions to the following problems; What is the inverse of a scalar $k$ in ECC? If I'm only missing ...
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518 views

ECIES vs. RSA + AES

I am confused about the distinction between RSA and ECC (Elliptic curve) regarding encryption and would appreciate it if someone could confirm whether my understanding is correct. To encrypt a large ...
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56 views

What factors do we take into account to compute the encryption and decryption time of an encryption/decryption algorithm?

I have been reading some papers on Image Encryption using ECC and chaotic systems such as 2D Arnold. What do they mean by 'Encryption ' and 'Decryption' time? How is it within 1 second? I tried ...
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219 views

The Generator point and Mod P in ECDSA

I've been reading about The discrete logarithm problem as of recent and i decided to try it out on a small portion of numbers myself and i actually came to a mental gridlock after watching this Video....
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35 views

Alter signature post signing without the private key

There a plethora of signature scheme's but I am wondering if there are scheme's with the following properties: Given that you know the message, alter the signature with the public key in such a way ...
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1answer
147 views

Solving Diffie-Hellman vs DLP

I'm wondering what is the current knowledge regarding the difficulty of solving the Diffie-Hellman problem (DHP). Obvisously solving the DLP (discrete log) is at least as hard as solving the DH ...
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52 views

Why is it necessary that the mod in an elliptic curve is a prime? [duplicate]

For the elliptic curve y^2 = x^3+2x+2 mod(23), why is it necessary that 23 is a prime. Why is the elliptic curve y^2 = x^3+2x+2 mod(24) not suitable for elliptic curve cryptography?
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129 views

How are the points in an elliptic curve over the finite field calculated?

For the elliptic curve with equation $y^2 = x^3 + x + 0 \pmod{13}$ in the finite field, how are all the points in this curve calculated. See the image below for an example created via https://graui.de/...
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50 views

How optimize elliptic curve point multiplication?

For 256 bits "Double-and-add" multiplication uses about 128 addings and 256 doublings, where "Montgomery ladder" uses near 256 addings and 256 doublings. "Double-and-add" ...
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174 views

How to choose secp256k1 private key?

The private key is any random 256 bit (but smaller than prime p) number or must be prime or other condition? For selected $x$ can be found $y$ - decompressing key: ...
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2answers
131 views

Can the ECDSA still work without present of hashing function? [duplicate]

According to walkthrough steps for ECDSA topic from wikipedia as shown below, What if the impact if we don't apply the hashing function (highlighted in blue in the image) to the raw messages? Although ...
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115 views

Using different hashing function with ECDSA

I came across an IC device configuration & security flow and the details are illustrated in image below. I'm wondering must the ECDSA pair with the SHA Hashing function? Alternatively, what if ...
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1answer
188 views

What's the difficulty of using elliptic curves to design homomorphic encryption protocols?

I have recently been very interested in elliptic curves because they are a powerful tool in crypto, ECC, pairing, etc. However, it seems that elliptic curves are not popular in homomorphic encryption. ...
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1answer
44 views

BLS to Schnorr signature conversion?

Imagine a situation where a prover can only sign with BLS signature signing algorithm, a verifier can only verify with Schnorr signature verification algorithm. Is it possible to convert a BLS ...
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1answer
104 views

What is the use of pre-computed points in ECC?

I am trying to understand the use of pre-computed points in ECC for ECC signature, verification, key generation, and so on. After searching on the internet, I understand that pre-computed points aid ...
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1answer
124 views

TLS 1.2 Server Key Exchange problem

Below the Wireshark snapshot of the handshake compliant to the TLS 1.2. The position 1 displays the enum ServerECDHParams where I can use any curve having the own ID RFC8422. I'm free for example to ...
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1answer
96 views

Using Optimal Prime Field in ECC

"Optimal Prime Field is a family of 'low-weight' prime fields that allow for efficient software implementation of all operations requiring a modular reduction, in particular the field-...
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1answer
238 views

What is the difference between anomalous elliptic curve and ordinary elliptic curve?

Probably this is a silly question but an anomalous curves and ordinary curves are the same things?
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1answer
99 views

ECC twin diversify

During my implementation of CommonCrypto from iOS, I noticed there is a function called CCECCryptorTwinDiversifyKey whose description is: Diversifies a given EC ...
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1answer
85 views

How long to reestablish PKI if Diffie Hellman and Factoring are in classical $P$?

Supposing there is a classical (no need quantum) $O(\log N)$ algorithm to factor integers $N$ and supposing there is a classical (no need quantum) $O(\log p)$ algorithm to find $g^{xy}$ given $g^x$ ...
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285 views

ECDSA signature generation and verification latency

I am performing some measurements of P256 ecdsa signature generation and verification latency and I was expecting that the signature verification will be faster than the signature generation, but is ...
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92 views

Constant time arithmetic implementation in DSA

I am trying to understand why it is a hard problem to have formally verified constant time arithmetic for DSA when compared with ECDSA. For instance, in ECDSA implementations of OpenSSL, we have ...
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1answer
164 views

Cryptographic limit to total accounts in secp256k1

Factoring in birth day attacks and all that, with 256-bit elliptic curve cryptography, lets take secp256k1 as example that Bitcoin uses, what is the maximum number of accounts that are secure? It isn'...
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1k views

What EC curve is used by Apple iOS platform?

I can't find information about EC curve used by Apple's iOS platform. The algorithm name that I could see in their docs is: ...
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1answer
202 views

Curve25519 Endianness

According to the original paper form Bernstein public/private keys and the shared symmetric key are stored in little-endian. However, the WolfSSL of WolfSSL supports both, little-endian and big-endian....
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1answer
167 views

Proof that user public key corresponds the curve equation (secp256r1)

I'm currently stuck at a problem, where I'm supposed to proove that the user public key of a returned u2f token corresponds to an elliptic curve equation (secp256r1). The token looks as follows: ...
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2answers
220 views

How to find the co-efficients of a function within Zp[x]?

I am a newbie in Finite Field arithmetic and while trying to implement an Elliptic Curve Cryptography based ABE scheme in a programming language, I am unable to understand how to implement function ...

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