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 ...

learn more… | top users | synonyms (2)

1
vote
0answers
23 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 = ...
0
votes
0answers
17 views

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 ...
0
votes
0answers
38 views

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 ...
0
votes
0answers
52 views

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 ...
2
votes
1answer
121 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. ...
3
votes
1answer
78 views

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/...
3
votes
1answer
48 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 +...
-1
votes
0answers
48 views

Computational Cost : Scalar Multiplication vs exponentiation in elliptic curve

$Pub=\gamma P$ and $Pub=P^{\gamma}$ where $P \in G_{1}$ and $\gamma \in Z_{p}$ Which one has less computational cost?
1
vote
0answers
33 views

How to set attributes to private key on PKCS#12 (key usage)

I make a certificate X509 with library Bouncy Castle on Java. I need set a Key Attribute to private key. ...
4
votes
2answers
90 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 ...
2
votes
0answers
29 views

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 ...
4
votes
1answer
41 views

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? ...
0
votes
1answer
30 views

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?
5
votes
1answer
225 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,...
1
vote
0answers
33 views

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. $h(.) : \{(x,y) \in E_p(a,b)\} \rightarrow \mathbb{Z}$
0
votes
1answer
17 views

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: ...
0
votes
1answer
44 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 ...
1
vote
1answer
67 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, $2P = (5,10)$. ...
11
votes
1answer
1k views

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 ...
3
votes
2answers
277 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?
1
vote
1answer
66 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 ...
2
votes
1answer
119 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 ...
1
vote
1answer
25 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 ...
0
votes
1answer
50 views

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.
0
votes
1answer
29 views

Is a KDF needed when using X25519 for ECDH and XChaCha20-Poly1305 for AEAD?

Is a KDF needed when using X25519 for ECDH and XChaCha20-Poly1305 or XSalsa20-Poly1305 for authenticated encryption? My hypothesis is "no" because the key from X25519 is less than 256 bits long; ...
0
votes
0answers
35 views

Has anybody implemented BGN cryptosystem to multiply two plain texts?

I have tried to use this code as follows, http://stackoverflow.com/questions/33581962/bgn-implementation-in-java but the issue is, when it generate the pairing, the output is in GTfiniteelement (for ...
2
votes
1answer
63 views

Multiplying integers modulo $2^{255}-19$ using the Curve25519 polynomial reduction algorithm

I'm reading the Curve25519 paper and I see that in page 11, under the title "Multiplying integers modulo $2^{255}-19$", it says: The coefficients of $x^{10}$; $x^{11}$; ...; $x^{18}$ in $uv$ are ...
-2
votes
1answer
24 views

How to find HEXA value of String [closed]

This may be very easy thing, but i am just unable to understand this. I have a string "Hi", and in HEXA its written like this ...
7
votes
1answer
189 views

How many qubits are required to break RSA 2048 or 4096 with a universal quantum computer?

So in the news this week, IBM have created a universal quantum computer with 5 fully functional qubits. Logic and Moore's law dictates they will be able to scale this up to a lot more qubits within a ...
3
votes
1answer
73 views

ECFP harder than ECDLP ?

Given two points $P$ and $Q = \sum_{i=1}^{n} x_i.P$ over $E_p(a, b)$ for $x_1,x_2,...,x_n \in \mathbb F_p$. The Elliptic Curve Factorization Problem (ECFP) is to find the points $x_1.P,x_2.P,...,x_n.P$...
0
votes
0answers
47 views

Weil Pairing - Miller's Algorithm

I'm trying to implement Weil Pairing using Miller's algorithm. I have got couple of questions. How to select $m$? As stated in this link page 13, I interated from $1$ to order of point $P$ such that ...
6
votes
1answer
100 views

Is every point on an elliptic curve of a prime order group a generator?

If the order of elliptic group is prime then every point is a generator of that group. I tested the above statement on some elliptic curves and found it true. Does that really work on all curves? Is ...
5
votes
1answer
107 views

Backdoor in NIST elliptic curves

Let $E$ be an elliptic curve defined over a finite field $F_q$ with prime order $n$ and $P,Q \in E$ and $k$ be private key such that $kP=Q$. Since $n$ is prime, $E$ is isomorphic to $Z_n$. Suppose $\...
0
votes
0answers
58 views

Smart Card choice for PKI implementation

I'm seeking to implement a national digital signature standard on a smart card. I feel like this is a good place to ask if anybody is acquainted with a hardware supplier offering smart cards that ...
4
votes
0answers
45 views

EC Schnorr signature: multiple standard?

I 'm working on some EC-Schnorr signature code. Reading various papers on that, it's seems EC-Schnorr is not standardized as well as ECDSA. For example, I found two main differences in two main ...
1
vote
1answer
40 views

Attacks on schemes based on elliptic curves when the transmitted points are not on the curve

Some elliptic curve schemes require to send a curve point during the normal execution of the protocol. For example, ElGamal encryption and ElGamal signature require this. On the other hand, ECDSA does ...
2
votes
0answers
31 views

Some confusions about Repeated Doubling Algorithm?

The following repeated point doubling algorithm is taken from the book Guide to Elliptic Curve Cryptography by D. Hankerson, A. Menezes, and S. Vanstone on page#93. Clearly, this algorithm is ...
6
votes
2answers
104 views

Is there a theorem to determine the elliptic curve parameters based on the group order?

By Hasse's theorem we know that range of the group order of the elliptic curve. And similarly, there exist a theorem on the admissible order of elliptic curves. Suppose by the theorem on the ...
0
votes
1answer
28 views

Is it possible for the Rho method against an Elliptic Curve to take more than the sqrt of the total state space?

Is it possible for the Rho method against an Elliptic Curve to take more than the sqrt of the total state space? It the reason why this is not generally done because of a meet-in-the-middle attack?
0
votes
2answers
58 views

Stripping off message authentication or signature

If attackers can strip off RSA / EC / -DSA digital signature and conduct CCA on AES-CTR or CBC payload, why can't they do the same for AES-GCM?
0
votes
1answer
80 views

What is necessary for generating an elliptic curve?

Let's say I want to generate my own elliptic curve with an order whose bit length is $n$ (specifically 2048, 4096, and/or 8192)? How would I do this? What needs to be done? What software can do this? ...
5
votes
0answers
59 views

Software timing attack using Kocher method

What's the minimum number of random sample points needed in Kocher's timing attack, so that we can determine enough valid measurements of $A_{i,r}$ and $D_{i,r}$? I'm working from this paper: Volker ...
1
vote
1answer
64 views

Does OpenSSL apply ASN1 encoding to the hash before signing using ECDSA?

I read on stack overflow that OpenSSL performs ASN1 encoding to the hash before signing it for, for ECDSA. In other words, OpenSSL performs the following steps when for an Elliptic curve key ...
0
votes
0answers
38 views

How common are non-RSA digital certificates?

Is there a statistic available that shows just how common are DSA or ECC certificates amongst webservers? I know that RSA-based certificates are the most common, however I'd like to know, if there is ...
3
votes
0answers
34 views

Is an instruction similar to PCLMULQDQ valuable in post quantum key exchange?

This paper describes a Quantum Key Exchange based on the Ring Learning With Errors problem. When used with ECC, there is only a slight performance impact. Assuming this is the popularized approach ...
0
votes
2answers
83 views

Is the Discrete logarithm problem suitable for this pairing scheme?

Let $Ans$ be the product of two pairings : $e(g,h)^{k} \times e(g,h)^{r}=Ans$ If everybody knows only $[g,h,e(g,h)^{k}]$ but $[r,Ans]$ is not known. In the discrete logarithm problem, the user knows ...
3
votes
1answer
34 views

Reuse of TLS client key/certificate in challenge-response protocol

The situation: We have a custom PKI with clients communicating with the server over standard SSL/TLS encrypted channel. PKI uses ECC, server certificate supports ECDHE_ECDSA key exchange mechanism and ...
4
votes
2answers
107 views

If we should not reuse primes in DH, shouldn't we not reuse ECDH elliptic curve properties?

An article How is NSA breaking so much crypto? describes NSA's methods for breaking encryption. If a client and server are speaking Diffie-Hellman, they first need to agree on a large prime number ...
-1
votes
2answers
55 views

elliptic curve point doubling in Jacobian coordinates

I am writing an application that uses Elliptic curve Diffie–Hellman for authentication. I found two formulas for point doubling in Jacobian coordinates. 1st) \begin{equation} X_1 = (3x^2 + aZ^4)^2 -...
0
votes
1answer
50 views

Proper forward secrecy [closed]

Currently I have a protocol using a simple RSA to AES handshake. I have been reading more and more and would like to implement proper forward secrecy, but at the same time I'd like to improve the ...