# 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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### What is the recommended minimum key length for ECDSA signature

I want to identify the proportion of certificates that use unrecommend ECDSA key length for TLS certificates based on some data I collected. By looking at a standard like NIST for example, I find ...
105 views

### Can I know from a Bitcoin public key if the private key is odd or even?

Can I know just from a Bitcoin public key if the private key is odd or even? [moderator note] That is, can we find parity of the private key from a secp256k1 public key?For the original dump of ...
50 views

### Convert secp256k1 private key to sr25519 private key

Is it possible to convert secp256k1 private key to valid sr25519 key?
68 views

### Would being able of factoring integers efficiently have some consequences over Elliptic Curve Cryptography?

Let's assume you can factor integers in a very efficient manner. Would that endanger the security of e.g. elliptic curve cryptography, or is there no link between the two ? You can often read that ...
245 views

### Are EC public key values evenly distributed?

At my Day Job(tm) we've encountered a bug wherein if the leading byte of the X or Y value of a public key are zero, "shit happens" (this bug is in our code - I'm not suggesting there's some ...
104 views

### Two Elliptic Curve Points having the Same X coordinate

Suppose in a elliptic curve (say the curve equation is: $y^2 = x^3 -17$) with prime order $q$, we have $(x,y_1) = nP$, where $P$ is a generator and $n<\lceil{q/2}\rceil$. Can we claim that there ...
850 views

### What is the difference between "Elliptic Curve Function" and "Hash Functions" like SHA256?

I am reading about bitcoin and I am a little confused about "elliptic curve function" and "SHA256". Do they have the same properties? Can both be used to generate private and ...
4k views

### Complete Set of Test-Vectors for ECDSA secp256k1

Although there are several implementations of ECDSA secp256k1 public available over the internet (the most popular being OpenSSL), it seems that there are no complete set of test-vectors available. ...
18k 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 ...
2k views

### Why does Smart's attack only work on anomalous curves?

Nigel Smart's attack solves the discrete logarithm problem in linear time. It requires the curve, however, to be anomalous, i.e. to have a trace of Frobenius equal to one or, equivalently, to be of ...
245 views

### Sextic twist over BN elliptic curves

I am struggling to understand how to perform a sextic twist over a BN elliptic curve. This is what I understood so far: Let's consider a BN elliptic curve: $$E: y^2=x^3+b$$ And let's consider a ...
3k 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, ...
551 views

### What crypto system allows for 3 parties: Party 1 who makes an assertion, Party 2 mutates the assertion, Party 3 validates it

I'm looking for the cryptographic equivalent of a Drivers license where the issuer can be verified, the issuer doesn't need to know who you showed the drivers license to, but also allows per-...
38 views

### Birational transformation from Edwards curve with not square d to Edwards curve with square d

How can I transform a complete twisted Edwards curve $ax^2+y^2 = 1+dx^2y^2$ with not square $d$ and square $a$ into an isomorphic Edwards curve $X^2+Y^2 = 1+DX^2Y^2$ with a square $-D$ i.e. $D = -r^2$?...
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### Is it possible (and if so how) to make one proof for multiple private keys in ECDSA

Lets say I have a message that needs to be signed by two keys that were generated using ECDSA Is it possible to make a signature that accounts for both keys, meaning I can verify with both and see ...
61 views

### ElGamal with elliptic curves and semantic security

To encrypt a group element $P$ with public key $K$ and randomness $r$ using ElGamal on elliptic curves with base point $G$ we do the following $(c_1, c_2) = (r\cdot G; P+r\cdot K)$. When we want to ...
76 views

### Are there any public keys for which the private key can be easily derived (ECDSA)?

I know that generally it's infeasible to find the private for any given public key. But I also came across the question "Find ECDSA PrivKey to PubKey = 0", in which it was explained that the ...
64 views

### What is/was SEC#1 ECC public key leading octet 0x01 for?

In the SEC#1 elliptic curve cryptography standard, the encoding of the public key involve a leading octet: 00h: The public key is the point at infinity. 02h, 03h: The public key is the compressed ...
20 views

### running Project Wycheproof against crypto implementations in languages other than Java

So I guess https://github.com/google/wycheproof "tests crypto libraries against known attacks". It appears to mainly be intended for Java crypto providers but can it easily be adapted to be ...
39 views

### Why does ECDSA produce a pair of values in its' signature (r,s)?

I was wondering why ecdsa generates a signature in form of a pair (r and s) and why it can't be only one value.
278 views

### Scalar multiplication with projective coordinates

I'm implementing point addition, doubling and scalar multiplication using projective coordinates. I took reference from this link. I have implemented Routine 2.2.6 (ec_double) Routine 2.2.7 (ec_add) ...
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### Multiuser encryption, singleuser decryption [duplicate]

I have an hybrid encryption (RSA, AES) for a file sharing project I am working on, where I use a single public key for encryption on the sender side and corresponding private key for decryption on the ...
64 views

### ECDSA - generating a new private key each time we sign?

So, I kinda get the mathematics behind the ECDSA, but I can't seem to find precise information about private key generation. In other words, do we have to generate private key, each time we generate a ...
106 views

### Size of group elements in a bilinear context

In a asymetric pairing context, which size (in bits) should have the elements of $\mathbb{G}_1,\mathbb{G}_2$ and $\mathbb{G}_T$ if we consider the most efficient elliptic curves?
108 views

### What is the meaning of $F_{p^k}$ and the elliptic curve over it, $E(F_{p^k})$?

In pairing based cryptography, there will be the finite field $F_{p^k}$ where $p$ is prime number and $k$ is an integer. The elliptic curve is constructed on that finite field as $E(F_{p^k})$. For ...
566 views

### 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 ...
124 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 ...
3k views

### What are the differences between ephemeral-static ECDH and static-static ECDH?

As I know ECDH can be used with a fixed public key. I read there are two types of static ECDH, ephemeral-static ECDH, and static-static ECDH. What are the differences between these two types?
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### kleptography SETUP attack in ecdsa

I'm trying to implement kleptography SETUP attack of ecdsa with python. Just a simply script to verify the algorithm. However i can't get the right output as the paper said. Where is the problem? Can ...
53 views

### Isomorphic mapping of BLS12-381 G2 points to G1

I'm attempting to reproduce ring signatures as described in Section 5 of https://crypto.stanford.edu/~dabo/pubs/papers/aggreg.pdf but applied to the BLS12-381 system. One of the assumptions in their ...