# Tagged Questions

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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### 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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### How does encryption work in elliptic curve cryptography?

So I think I understand a good amount of the theory behind elliptic curve cryptography, however I am slightly unclear on how exactly a message in encrypted and then how is it decrypted. So my ...
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### Schnorr Ring Signatures - wrong hash results

I don't know if I've placed the question right, It is half maths, half programming. I'm writing Schnorr Ring Signatures on Elliptic Curves in Java and I have a problem. I've found scheme on integers ...
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### Do I understand (below) why Q = dP is easy while finding d is hard

As we all know for discussion of Dual_EC_DBRG, the point on an elliptic curve Q can be calculated from P and some (large) integer d $Q = dP$ And we know that knowledge of Q and P is not sufficient ...
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### What happens if you multiply a point with its order on complete Edwards curves?

I was recently working with some ECC crypto and stumbled across the following phrase on the SafeCurves page: The rational points of a complete Edwards curve are the pairs (x,y) of elements of ...
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### What is the most secure ECC Curve?

I have for a while used Koblitz curve (sect571k1), in ECDH and ECDSA. But I have started wonder if it is the most secure. I prefer security over efficiency. So the curve doesn't have to be the most ...
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### How do I get the equivalent strength of an ECC key?

I know how to calculate the comparable symmetric strength of an RSA modulus: calculate the running time for a field sieve. This is how NIST gives approximate symmetric sizes for asymmetric algos in ...
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### HD (Hierarchical Deterministic) Keys using Safe Curves?

Bitcoin's HD (Hierarchical Deterministic) Keys as described in BIP32 allow for a master key to be created (a private key and a chain code) such that a tree of both public and private keys can be ...
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### Translation of Schorr Ring Signature to ECSchnorr Ring Signature

I have to write an EC version of Schnorr Ring Signature Scheme. I've already wrote regular ECSchnorr Signature Scheme using this (page 128). I've found a scheme of Schnorr Ring Signature Scheme (page ...
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### Elliptic Curve ElGamal and DSA - smooth group order and element of large prime order

In regular ElGamal and DSA, we choose large primes $p$ and $q$ such that $p\equiv 1\pmod{q}$, and a group element $g$ of order $q$ by computing $a^{(p-1)/q}$ for some random $a$. This is to prevent ...
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### Seeking an implementation of the Satoh algorithm for elliptical curve point counting

I would be very grateful if someone has an implementation of the Satoh algorithm (Fast Elliptic Curve Point Counting). Can someone point me to practical algorithm implementations or provide some ...
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### How to compute projective cordinate Z in elliptic curve cryptography?

I was working on affine coordinates and struggling with the computation time taken for operations and then I was advised to use projective coordinates so that mul-inverse operation can be avoided Can ...
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### Is it possible to re-generate ECPublic key from raw private key and curve params?

As per my understanding, in Elliptical curve cryptography, the EC PrivateKey is nothing but a bigInteger value. If you know the curve specs and you have this private BigInteger value (which I am ...
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### Is there any alternative for extended euclidean algorithm to perform modulo division?

I'm implementing point addition and point doubling operations for elliptic curve cryptography. I have implemented extended euclidean algorithm to perform modulo division. It appears the that ...
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### How to perfrom modular division while numerator is lesser than the denominator?

I'm implementing point addition and point doubling of elliptic curve cryptography. The formula that I'm using for slope is Point addition: $S = \frac{(P_y-Q_y)}{(P_x-Q_x)}$ where $P$ and $Q$ are the ...
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### Optimal same-base exponentiation?

I've (finally) implemented the answer to this question in our library, which stated how to transform montgomery curves (and points) to weierstrass curves (and points). Now, for scalar multiplication, ...
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### elliptic curve multiplication with negative factor

I'm learning the multiplication operation on EC. From most material I can found, the multiplication $nP$ is just: $$nP=P+P+\cdots +P+P$$ For negative factor, i.e. $(-n)P$, by above definition and the ...
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### A standard extension of ECIES for multiple recipients (broadcast / multiparty)?

I have one sender, and a small number (~5) of recipients. The sender knows each recipient's public EC key. I want the sender to broadcast a single message in such a way that any one of the recipients ...
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### Cryptographic operations for NISTP256 can be implemented using montgomery method?

I need to implement cryptographic operations starting with the curve NISTP256. I have been told to implement it using Montgomery method. I read a pfd from http://saluc.engr.uconn.edu/refs/sidechannel/...
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### RSA & DH at risk due to math advances, will this eventually affect elliptic curves too?

I was looking into the predictions by some researchers that RSA and Diffie-Hellman may not be secure in the next few years due to advances in math and being able to calculate the discrete logarithm ...
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### Edwards / Montgomery ECC over binary extension fields

I recentely had a discussion about the redesign of our ECC code for the library I'm collaborating on and the person I was discussing with came up with Edwards and Montgomery curves over binary ...
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### ECC keys vulnerable to brute force attack?

I have started learning about Elliptic curve cryptography. Since the key size required in ECC is relatively lesser than the key size in RSA to provide the same amount of strong encryptions, I wonder ...
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### Elliptic Curve Blind Signature Implementation

I have seen this prior post: Elliptic Curve based blind signature implementation Currently I'm sizing up how difficult it would be to attain Elliptic Curve Blind signatures for an application I'm ...
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### 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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### 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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### Is there any reason not to use EdDSA with Weierstrass curves?

I'm volunterely working for a crypto library and we're planning on adding Curve25519 support (finally). At the same point I had the idea of adding support for EdDSA in the same run. Our library is ...
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### 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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### 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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### 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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### 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: $P = prv*Q$...
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 $... 2answers 60 views ### How does the size of the prime affect Elliptic Curve Bit Security? I am using the MIRACL Library to implement an Elliptic Curve Diffie Hellman based Key Exchange according to ECDH-Scheme-Wikipedia. Referring to the Miracl Docs they suggest a few curves. Each curve ... 2answers 49 views ### With EC secp256k1 is there a way of transforming a function of the private key to a function of the public key? A key pair has a private key$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)$which can be transformed into a ... 1answer 173 views ### With ECDSA is there a way for the verifier to calculate any properties of$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, ... 3answers 346 views ### Is there a 1:1 mapping between private and public EC keys? After asking: Are all possible EC private keys valid? I learned that all 32 byte (256 bit) values greater than 0 and less than n are all valid private keys. This means that 99% of all 256 bit values ... 2answers 422 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 ... 1answer 78 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 ... 2answers 118 views ### Is signing a plaintext sufficient? If I have N bytes of plaintext, does signing it with my private key prove (to holders of my public key) that I have signed that exact plaintext messages? i.e. could an attacker use the plaintext and ... 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 ... 1answer 40 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 ... 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 ... 2answers 178 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 ... 1answer 349 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, ... 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 ... 1answer 74 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=...
I have calculated the affine points on the curve $x^2 + y^2 = 1 − 3x^2y^2$ over the field ${\mathbb{Z}}_{11}.$ Using $y^2 = \frac{1-x^2}{1+3x^2}$ I got the following points: \$(0,1),(0,10),(1,0),(2,2)...