# 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 ...

0answers
54 views

### 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 ...
1answer
72 views

### 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 ...
0answers
35 views

### 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 ...
0answers
67 views

### 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 ...
0answers
35 views

### 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 ...
3answers
148 views

### 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 ...
1answer
76 views

### 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 ...
1answer
64 views

### 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, ...
1answer
42 views

### 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 ...
1answer
56 views

### 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 ...
0answers
66 views

### 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/...
4answers
1k views

### 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 ...
0answers
32 views

### 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 ...
1answer
412 views

### 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 ...
0answers
50 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 ...
0answers
39 views

### 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 ...
2answers
81 views

### 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 ...
1answer
93 views

### 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 ...
0answers
40 views

### 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 ...
0answers
17 views

### 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 ...
1answer
80 views

### 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 ...
0answers
54 views

0answers
39 views

### 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: $P = prv*Q$...
1answer
42 views

1answer
89 views

1answer
105 views

### Can a billion elliptic curve keys be generated on a laptop in less than an hour?

I want my application to generate an EC key pair. The first four bytes of the sha256 hash of the public key should contain a known IP address. As hashes are one-way functions, I need to brute force ...
1answer
274 views

### ECDH or RSA more secure for symmetric key wrapping?

Suppose a message is encrypted with a symmetric block cipher with a random key. RSA is often used to wrap the symmetric key using the recipient's public key. In this case, the size of the message is ...
0answers
56 views

### Using a product of a series of curve25519 scalars as a private key

There are a few systems like the GNU Name System and the Sphinx mixnet packet format that employ a series of curve25519 scalars all multiplied together as a private key. Are there any caveats to ...