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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Finding Elliptical curve points and encoding text using them

I recently got into learning Elliptical curve cryptography and are currently building a project in C#. Everything is working well so far, I can encode and decode points, and thanks to this forum I ...
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How can I find all points on an elliptic curve?

I have an elliptic curve $$y^2=x^3 + 8 \times x + 6 \mod 13$$ How do I find all the points on this EC? Also, could you give me more examples?
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232 views

Key exchange using ECDH vs ECIES?

I'm a beginner to ECC crypto programming. Does any one explain to me the difference with using ECDH for shared key exchange and use of ECIES by encrypting shared key with the public key of the ...
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What is proper size of window Using RSA Window method?

I want to Use Window method for RSA modular Exponentiation. because of SCA. But I don`t know what is proper window size.
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311 views

Simple digital signature example that one could compute without a computer?

I am working on a document to explain Bitcoin to students. But I am having a hard time translating the principle described in §2 of the Bitcoin whitepaper in layman's terms. There is a great question ...
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124 views

Do I need to prove this?

I am using ABE scheme that has already proven under BDHE assumption. Here is the scheme https://eprint.iacr.org/2008/290.pdf In the key generation algorithm, I want to tie the user secret key ...
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407 views

How to measure ECC key size?

I have implemented a ECC key generation scheme successfully. Now I need to find ECC key sizes of each generating key pairs. I assumed that ECC key size is the size of the ECC private Key. So I would ...
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64 views

Given $ g^s, g^y , g^r, g^t, g^{st-rs}, g^{(yr+d)/t}$ , is it hard to distinguish $e(g,g)^{syr}$ from a random value?

Where $g$ is a group element in bilinear group $G$, $e(g,g)∈GT$ and $s, y, r, t, d$ are randomly chosen. I understand it is very similar to the conventional DBDH problem, but $g^t, g^{st-rs}, g^{(yr+...
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41 views

Given $g^a, Y$, is it hard to distinguish $e(g,g)^{ab}$ from a random value?

where $g$ is a group element in bilinear group $G$ $Y = M.e(g,g)^{ab}$ $M$ is a message Does anyone know the answer or suggest some material for reference? Many Thanks
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Using a single Ed25519 key for encryption and signature

The libsodium documentation contains a function crypto_sign_ed25519_pk_to_curve25519 that converts an Ed25519 key into a Curve25519 one, so it can be used for both ...
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21 views

Time efficiency of Bitcoin Multi-signature Vs. threshold signature

I read this paper (Securing Bitcoin wallets via a new DSA/ECDSA threshold signature scheme) that illustrated that threshold signature is the best solution to avoid single point of failure but I think ...
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555 views

Can elliptic curve (25519) be used to encrypt file?

This is probably a simple question, but I haven't been able to see it stated anywhere. Is it possible to directly encrypt a file (of any length) with some form of EC using the 25519 curve. I know it'...
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65 views

security of using digital signature as key derivation material

I want all keys in my iOS application to rely on the Secure Enclave for security as the iOS keychain becomes insecure on jailbroken devices. Currently, the Secure Enclave currently only supports ...
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2answers
664 views

Creating serial key generator using ECDSA, how to get signature short enough?

I've written some questions in this stackoverflow and got great responses but now I'm trying to wrap it all together. I have for the last couple of weeks been building a serial key generator project ...
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46 views

Is this ECDHE approach secure?

First of all sorry if this question could be trivial, but I did some researches and it seems to me that this is a standard approach, but I want to be really sure. I'm developing a signed/encrypted ...
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316 views

RSA and ECDSA Certificate Sizes

Is there a table (or a whitepaper from official sources) that compares the size of X509 certificates generated with RSA (starting from 1024 bits) and ECDSA (starting from 160 bits) ? Thanks for the ...
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73 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 is 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 ...
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What does Shor's algorithm tell us about the complexity class of RSA and the DLP?

If quantum computers operate in BQP and (using Shor's algorithm) they are able to factor large integers and break the discrete log problem, what does that tell us about the complexity class of these ...
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Why do openssl elliptic curve digital signatures differ by one byte [duplicate]

For some curves defined in Openssl 1.0.2h if I generate a key and generate a digital signature the size of the signature block changes by one byte. Why does this happen? My test file is, y.sh ...
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69 views

Is brainpoolP512r1 safe?

I'm using brainpoolP512r1 elliptic curve for DSA and DH in my application. Recently I've found out on this website that brainpoolP256t1 and brainpoolP384t1 aren't secure. Unfortunately my curve wasn't ...
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71 views

If I encrypt data with two different ECC Private keys, how secure is the result?

I'm wondering whether encrypting data with two different 256-bit ECC keys will result in a more secure encryption (minimum 384 bit equivalent) or will result in data that's effectively encrypted with ...
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70 views

Feasible attacks on ECRSA cryptosystem

In ECRSA cryptosystem, I want to know the feasible attacks. For illustrations we have two prime $p$ and $q$ such that $p \equiv 2 \pmod 3$, $q \equiv 2 \pmod 3$ and generate key pair as follows: $$n = ...
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elliptic curve and embedding degree

I am new in ECC. I am confused what the embedding degree in elliptic curve represents and what is the impact of its values on the curve and security ( small values or large values? What does the ...
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Found weil pairing. Index Calculus method on the results of weil pairing

Consider Elliptic curve with p = 59, A = 1, B= 0, P = (25,30) and Q=(35,31). So I tried to solve this using MOV attack. The torsion point for them E[5] is R(-25,30i) where is sqroot -1 Chosen two ...
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Why is RSA still being used? [duplicate]

In hybrid encrytion, I still see that some site's use RSA in their https connection, so now I wonder, why do they not use ECC instead of RSA, ECC requires less computational power and encrypt's and ...
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tripartite diffie hellman with Weil pairing

I try to understand how the tripartite Diffie-Hellman key exchange works. I read Joux's paper for this: https://www.semanticscholar.org/paper/A-One-Round-Protocol-for-Tripartite-Diffie-Hellman-Joux/...
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136 views

How does DH work when combined with ECC or RSA?

I know that Diffie-Hellman is used to create keys in a secure way over an insecure channel. But there is one thing which I cannot understand: I see that a lot of sites use ECC or RSA alongside DH. ...
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130 views

Quantum vs. regular computing time to break ECC?

How long exactly would it take for a regular computer to crack an elliptic curve public/private key via bruteforce, vs. a quantum computer using Shor's algorithm with a couple thousand qubits? Can ...
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53 views

Is a hash function used to expand the key after ECC shared secret is complete?

I am trying not to solicit opinions, but I have not been able to find a reference to the question at hand. I have designed an ECC engine in silicon that handles any curve in the form of $y^2 = [ax^3 +...
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2answers
104 views

Recover elliptic curve order from ECDSA signatures

I need the elliptic curve order to recover the private key from two signed messages with ECDSA. What I have: two signatures signed by the private-key I want to get the messages that have been ...
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75 views

Comparison Affine Coordinates and Projective Coordinates Addition in Excel

Kurve : EC : $y^2=x^3 + x + 1$ Generator:$(1,7)$ $p=23$ Result in Affine use Excel: $P=(1,7)$, $Q=(7,11) \implies P+Q=(18,20)$ Result in Projective use Excel: $P=(1:7:1), Q=(7:11:1) \implies P+Q=(15:...
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Attacks on elliptic-curve based cryptosystems through solving the Decisional Diffie-Hellman Problem with the Weil Pairing

Are there any examples of practical attacks on cryptosystems set over elliptic curves which utilize the easiness of DDH for certain choices of curves $E(\textbf{F}_q)$, and as such their lack of ...
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Boneh/Franklin Identity based encryption with Tate pairing

Boneh/Franklin developed an identity based encryption scheme based on the Weil Pairing. This algorithm has also been standardised in IEEE P1363.3 . I know that this algorithm can also be implemented ...
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Key derivation with Curve25519 for data encryption

I'm new when it comes to cryptography so this question might be a little bit stupid: Can I derive a key with Curve25519 from a (let's say) root key and encrypt the file with a secret key algorithm? ...
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meaning of Reduce f modulo the order of the base point G

I am trying to perform some math operations related to Elliptic curve cryptography, and came across this sentence: Reduce f modulo the order of the base point G. What does it mean?
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235 views

ECDSA key recovery - floating point values

I'm currently attempting to recover an ECDSA key. I have $m$, $m'$ and signatures $(r, s)$, $(r', s')$, and I know that $k$ is constant, the curve is NIST P-192 and the hash function of the. As such,...
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Default algorithm for scalar multiplication of elliptic curve points by the MIRACL Library

What is the default algorithm used by the MIRACL-Library [1] for elliptic curve cryptography systems to perform scalar-point multiplication with curves of Weierstrass form satisfying the equation : $y^...
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hash function for elliptic curve co-ordinates

Is there any hash function which takes the co-ordinates of an elliptic curve $E_p(a,b)$ as input and gives an integer value i.e. $h(.) : \{(x,y) \in E_p(a,b)\} \rightarrow \mathbb{Z}$
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How many field operations are needed when you compute kG in elliptic curves with a multiple additions or the double-ans-add-algorithm?

For an assignment, we have to calculate how many field computations are needed to calculate kG in an elliptic curve. They want us to show this for two different ways of calculating kG. The first way: ...
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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 ...
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227 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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71 views

Scalar Multiplication for Elliptic Curve

Let $\mathbb{E}$ be the elliptic curve $y^2 = x^3 + 6x \text{ mod } 11$ and consider the point $P = (2, 3)$ on it. How do I compute $3P$? I have been able to figure out what $2P$ is, $2P = (5,10)$. ...
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Why can an elliptic curve private key be 1?

I often see in papers (e.g. this one) that for an elliptic curve with generator point $G$ and order $n$ the private key $d$ can take on any integer value in the range $[1, n)$. When $d = 1$ the ...
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How to convert roots of Weber polynomial to Hilbert class polynomial over modulo prime?

Using any non square root discriminant $D$, we should be able to find the Weber class polynomial. How can I convert the roots of a Weber polynomial to a Hilbert class polynomial over modulo prime?
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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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307 views

Which elliptic curves are quantum resistant? [closed]

If I want to learn about quantum resistant crytography what are the best resources? Which type of elliptic curves should I be studying?
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93 views

Creating ECDH using OpenSSL

For academic reasons, I'm playing around with OpennSSL 1.0.2g. I tested RSA encryption/decryption. I created key exchange with DHKE. But I'm struggling to find a way, to create ECDH, using only ...
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Finding the subgroup in isogeny-based cryptography

Isogeny-based cryptography is one of the newest post-quantum cryptography. Hardness of this system is based on finding isogeny between two elliptic curves. Also this is theorem: Elliptic curves ...
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26 views

Single-scalar multiplication with sign bit

I want to know if there's an "easy" timing-free way to compute the sign of $y$-coordinate of $r G$, for a secret scalar $r$ and $G$ the generator of an elliptic curve. We have several choices for ...