The Stack Overflow podcast is back! Listen to an interview with our new CEO.

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.

Filter by
Sorted by
Tagged with
0
votes
0answers
76 views

TLS 1.2 handshake ECDH premaster/master secret generation with C OpenSSL API [on hold]

I am doing a study on the TLS protocol as my degree thesis, but being completely inexperienced on this subject, I have many questions. I have to write C code and program a client that partecipates ...
3
votes
0answers
46 views

Using (EC)DH to generate a signature

Say I have access to a system that is limited to performing (EC)DH, followed by key derivation to produce a secret key. This secret key can e.g. be used to generate a MAC. Is it possible to generate a ...
0
votes
0answers
6 views

Have someone replaced Curve25519 in NaCL library? [migrated]

I am using NaCL library and I like it but I wonder if it is possible to replace Curve25519 with different stronger Curve if stronger encryption is needed. I do understand that new library would be ...
0
votes
1answer
44 views

How to represent the point-at-infinity(Elliptic Curves) in code? [duplicate]

I am writing code for Elliptic Curve Cryptography. I have a class class EllipticCurvePoint. ...
2
votes
0answers
38 views

What are some use cases for white-box digital signatures?

There were 2 papers published in the last year, that describe 2 different white-box identity-based digital signature schemes: White-Box Implementation of the Identity-Based Signature Scheme in the ...
0
votes
0answers
5 views

Get X.509 Certificate ECDH private and public key on Android (Java/Kotlin) [migrated]

I'm currently trying to implement a ECDH algorithm in my android app. But I'm facing an issue, I would like to store the private and public key in Android KeyStore. However in order to achieve this I ...
0
votes
0answers
58 views

Is it possible to distinguish ECC private key from the random values

I have a list of the random values (each 65 bytes long). One of the items is a private key which is used to sign the data: ...
0
votes
0answers
36 views

EC threshold private key's multiplicative inverse and derived-key sharing

I have two devices, and each has a private key xPriv-i. Each device computes the corresponding EC public key xPub-i, shares it, and the linear combination of the keys is the "real" public key xPub. ...
3
votes
0answers
90 views

ECDSA signature verification checks

From Wikipedia: Check that $Q_a$ is not equal to the identity element $O$, and its coordinates are otherwise valid. Check that $Q_a$ lies on the curve. Check that $n*Q_a = O$ Verify that $r$ and $s$ ...
0
votes
0answers
43 views

Difference in elliptic curve order and finite field size [duplicate]

Must the prime finite field, Fp, an elliptic curve is defined over always have a greater number of elements than the cardinality of an elliptic curve. For example, If I have ...
1
vote
0answers
43 views

How to know if a point on a discrete elliptic curve be represented uniquely using its y-coordinate?

Let's say we have a point on an elliptic curve $p=(x, y)$ which is not the point-at-infinity. Can there be some other point $\hat{p} = (\hat{x}, y)$ that is also on the curve and that has the same y-...
1
vote
1answer
40 views

Prevent a Man-In-The-Middle attack whilst transmitting a PSK for first time

I'm developing a network where two parties that want to join both compute ephemeral ECC keys for a key exchange, to create an encrypted connection. I plan to authenticate these keys by signing them ...
0
votes
1answer
80 views

Group in the context of elliptic curve crypto [duplicate]

I understand that the discrete log problem is defined as $G^y \bmod p = x$ Speaking generally, $G$ here is a generator for the group zp*, where $G$ is able to ...
5
votes
1answer
409 views

Can multiple public keys lead to the same shared secret in X25519?

I have no mathematical knowledge about this, but I just read in RFC 7748 the following: Designers using these curves should be aware that for each public key, there are several publicly ...
0
votes
0answers
30 views

ECC order and modulus in EC [duplicate]

This question came from security.stackexchange.com. I have an error in reasoning regarding to the calculations on elliptic curves. The basic group operations are all calculated mod p. Ok right. Then ...
1
vote
1answer
39 views

Ensure Data Integrity In An ECDH Key Excange

Been playing around with the inner workings of onion routing and I have a problem. If I wanted to send the 2nd node of a relay network an ephemeral ECC public key, it has to go through node 1, so that ...
0
votes
1answer
35 views

Computing inverse of BN256 G2 point in golang x/crypto/bn256 library

I'm trying to confirm a vulnerability in a signing scheme I'm helping with. To do this I need to simulate a rogue key attack on a BLS aggregate signature using the golang bn256 library https://godoc....
0
votes
1answer
46 views

ECDSA secp256k1 attacks

Are there any known and feasible ECDSA attacks on secp256k1 which can reduce the bit security of the algorithm? For example from 256 bits of security down to 192 bits?
1
vote
2answers
64 views

How does ECDSA signature verify work in EOS and ETH/BTC, compare to standard (on text book I mean)

I have been studing ECDSA signature/verify for a while. By my understanding: the standard ECDSA signature/verify process (which we find on text book) are like below: - A sender combines message and ...
0
votes
1answer
67 views

Why we cannot brute force Elliptic Curve private key? [duplicate]

I am learning ECC, I am confused a bit how it works for now. To my understanding, G is the starting point, k is how many times you apply the dot operation. And <...
0
votes
1answer
40 views

ECDSA public key point uniqueness [duplicate]

I'm new to ECDSA and there is something I still not sure about. If I have a classic Certificate Authority server that delivers PEM certificates containing public key with ECDSA, I can retrieve the ...
1
vote
1answer
46 views

Efficient calculation of point coordinates with elliptic curves over binary field

I'm trying to find an efficient algorithm to calculate the $y$ coordinate of a an elliptic curve point given its $x$ coordinate, for elliptic curves over fields of the form $2^m$ with polynomial ...
1
vote
1answer
80 views

Calculation of the order of the cosets used in defining the Tate Pairing

I'm working through Pairings for Beginners by Craig Costello, and am trying to understand the preamble to the Tate pairing. (See p. 70 ff., section 5.2 of of the PDF.). I'm having trouble following a ...
-1
votes
1answer
57 views

Points on elliptic curve [closed]

I am making a program using the library cryptopp using curve secp521, in which at the end of that program I get n*Point Because I am writing that program I know that what is the value of 'n'. So, I ...
1
vote
1answer
61 views

What is the possibility of collision of trailing 160 bits of Keccak_256, for any two differing public-keys as pre-images?

Earlier today I was answering a question on the ethereum SE site that analyzed the potential for more than one private key on curve secp256k1 (which maps to a distinct public key) to control the same ...
0
votes
1answer
80 views

RSA vs Elliptic Curves

I am currently reading about how more efficient and ''light'' is ECC compairing to RSA as far as key generation is concerned. My question is simple, why does RSA continue to be used today (ex.SSL) ...
4
votes
1answer
127 views

Hash multiset to point on elliptic curve where $A = 0$

I want to hash a multiset to a point on the elliptic curve $y^2 = x^3 + 3$ over a finite field of some 254-bit prime order, where $P = 3 \pmod 4$. Moreover, I want this hash to be incremental, in that ...
2
votes
1answer
71 views

Elliptic Curve Discrete Log in a Composite Ring

Elliptic curves are usually defined over prime rings (fields), but what if we chose a ring of composite order? Let $n = pq$ for $p,q$ large primes. Say I have elliptic curve $y^2 = x^3 + ax + b$ over ...
0
votes
1answer
74 views

Learning elliptic curve cryptography for specific application

I would like to develop a protocol for specific purpose. This protocol will utilize asymmetric cryptography in which one private key can be paired with numerous public keys: messages encrypted with ...
4
votes
1answer
95 views

secp256k1 point density

I am working on a crypto project using the secp256k1 elliptic curve. I know that I can select a random point $P = (x, y)$ from the curve by randomly selecting the first coordinate $x \in \mathbb{Z}_p$...
0
votes
1answer
71 views

Elliptic curve with prime subgroup equal to field size

I am aware that when the equation $\#E(\mathbb{Z}_p) = p$ holds for prime $p$, the elliptic curve is called "anomalous" and is insecure do to "Smart's attack". Consider the similar case that $E(\...
1
vote
2answers
76 views

Using public-key signature instead of having API key

I am designing an application that will need an API key. At first I believed that generating a long, random token would be secure enough (say 32 chars string that includes 0-9, a-z and A-Z), and then ...
1
vote
2answers
69 views

“Dave Check” for a tweakable P-256 ECDH KDF

I have two devices with hardware tokens that contain P-256 private keys, and which allow me to compute ECDH shared secrets with arbitrary public keys. I need to build a tweakable key derivation ...
0
votes
2answers
93 views

Discrete logarithms on elliptic curves

In many examples of attacks on public key cryptography, examples of the form $a ^ x = b$ are used, but I can not understand the correlation between this and the multiplication of the generator point ...
-1
votes
1answer
75 views

P256 Key size and validation [duplicate]

Given a public key on the P-256 Curve is it correct to say that the public key is 64 bytes long ie. (x,y)? Secondly is the private key 32 bytes long? if so, how is the private key generated and why ...
0
votes
0answers
33 views

Is there an O(1) in space complexity k-of-n signature scheme?

I was looking in depth into Schnorr signatures recently, and while they are very attractive for their ability to be aggregated, this only works for n-of-n ...
0
votes
1answer
83 views

Is that possible to calculate modular inverse of a point on elliptic curves?

Imagine that you are given a point $P$ so that $P=a\times G$. If you have no knowledge of $a$ is that possible to calculate point $I$ so that $I$ is the modular inverse of $P$? We know that over ...
2
votes
1answer
94 views

Is there any asymmetric encryption algorithm for eliptic curve(secp256k1) without AES? [duplicate]

I am looking for asymmetric encryption using SECP256K1. But all over the internet, I see that it also requires AES encryption. Instead of generating an AES secret key, is it possible to encrypt using ...
0
votes
0answers
36 views

ECDSA dA multiplication algorithm [duplicate]

I was looking at this question and i can`t understand this part: QA = dA G = 5 (5,1) = (9,16) I saw that algorithm used for this was Double-and-add algorithm but i didn't get it. Can ...
2
votes
2answers
116 views

Talking TLS with EC cryptography and the secp256k1 curve [duplicate]

How reasonable would it be to speak TLS over the secp256k1 curve? My initial experiments show that OpenSSL supports it (albeit with special flags, see below): Running an OpenSSL client against an ...
4
votes
2answers
563 views

ECDSA: Why is SigningKey shorter than VerifyingKey

Total Crypto Noob here. I was wondering why in ECDSA the Signing Key is so much (half of) shorter than the Verifying key? Lets look at some python code: ...
0
votes
1answer
53 views

Elliptic Curve Cryptography messages vs keys encryption [duplicate]

I have read a few tutorials about ECC implementaiton in C. What I am confused is this: Can I encrypt messages with ECC and without the use of any other algorithm, like AES, RSA or should I use them ...
1
vote
1answer
56 views

ECDH for more than two parties

With classic diffie-hellman it's possible do it with more than two parties. Is this applicable to elliptic curve diffie hellman? I'm guessing not. With ECDH you have a scalar number as the private ...
1
vote
0answers
59 views

GPG implementation of ECC “Encryption” (ECDH) vs RSA

My understanding of GPG with traditional RSA keys, is that RSA is by definition can be used to both sign and encrypt. This is because RSA can be directly applied to plaintext in the following form: <...
1
vote
0answers
50 views

How to use Montgomery arithmetic for elliptic curves (FIAT cryptography)

Let us consider the source code for curve P-256 from BoringSSL. This source code can be found here. This source code uses the FIAT generated implementation for field arithmetic. This implementation ...
1
vote
0answers
37 views

Is ECC multiplication over real number also one-way? [duplicate]

ECC multiplication over GF(p) is clearly one-way. How about ECC over real number? Is ECC division over real number also practically impossible?
5
votes
2answers
948 views

Raw curve25519 public key points

I'm trying to understand curve25519, and ECC public points. I'm playing with Minisign, to better understand the fundamentals of ECC. Minisign uses curve25519 and outputs public keys as base64 ...
1
vote
1answer
55 views

CSR signature using elliptic curve [closed]

We've been asked to generate a certificate signing request using elliptic curve and we can't use any third-party library as it's an embedded application with very limited resources). We are used to ...
0
votes
0answers
28 views

ECDHE Key with KDF Necessary [duplicate]

Is it necessary to pass a ECDH generated key to a KDF? According to the python cryptography documentation, it is stated that For most applications the shared_key should be passed to a key ...
1
vote
1answer
67 views

Point doubling with only one coordinate

In many source codes that implement ECDH, there is a function that multiplies the base point of that curve with a constant. This function usually takes as arguments the constant and just one ...