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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Second generator for secp256k1 curve

I want to get a group element $h$ on the elliptic curve secp256k1. The important thing is that no one should know the discrete logarithm of $h$ with respect to $g$. That is, $h$ should be created from ...
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2k views

Why is the P-521 elliptic curve not in Suite B if AES-256 is?

In the NSA's document, "The Case for Elliptic Curve Cryptography", we have ...
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99 views

What does signed fixed window method mean in ECC?

I am studying (sliding) window method in Elliptic Curve Cryptography (ECC) but I am confused by the term, signed fixed window method. By the way term is used in a research paper and not in the book ...
3
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1answer
82 views

Non adjacent form of an integer is unique

I have tried to look up the proof for NAF (Non-adjacent form) being unique for every integer, but as far as I have seen, textbooks only mention it as a property of NAF, but no proof is given. Also I ...
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34 views

Generating interactive, secure multiple ECC key pairs deterministically

In Elliptic Curve Cryptography (ECC) assuming user A has a private public key pair of $S$, $P$ accordingly with generator point $G$ which as we know is: $$P=S*G$$ Assuming that user A wants to ...
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193 views

Elliptic curve cryptography G*G

I understand how ECC works for the point multiplications and stuff. All we normally do is to multiply a scalar number (lets say d as a private key) with the base point generator ...
8
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563 views

How does ECDH arrive on a shared secret?

I read a brilliant, three part article on Elliptic Curve cryptography (one, two, three). It was able to explain Elliptic Curves to me in a way that didn't require a math degree to understand. The ...
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1answer
64 views

Is there any patent free EC point compression available? If not, should I GPL/LGPL my code?

I'm currently using the BouncyCastle implementation in uncompressed mode, and considering releasing an optimized version of EC code that uses point compression. It appears the only thing limiting me ...
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100 views

Is it ever unsafe to compress an EC point?

I am working with a library that outputs EC points in uncompressed form. To save space, I'm considering modifying said library to use compressed EC points. Assuming that I keep track of the sign bit ...
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607 views

Compressing EC private keys

For reasonable security, EC private keys are typically 256-bits. Shorter EC private keys are not sufficiently secure. However, shorter symmetric keys (128-bits, for example) are comparably secure. I ...
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35 views

EC based password authenticated key exchange protocol

I would like to know: What is the currently best (efficiency and security wise) known EC based password authenticated key exchange protocol? (i.e. is there any EC based protocol may be similar to DH ...
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66 views

Popularity of ECMQV authenticated key agreement protocol

I've got a few ECMQV related questions: Why is ECMQV a more efficient EC-based authenticated key agreement protocol? Why is ECMQV so popular? Is it because no other protocol of its strength exists? ...
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228 views

Elliptic Curve Crypto, is a distributed signing method possible using Shamir's Secret Sharing?

Note: A distributed signature scheme exists for RSA: Practical Threshold Signatures, Victor Shoup. Is it possible to adapt such scheme for ECC? A centralized signing machine is vulnerable to ...
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1answer
50 views

Average/approximate difference in value between valid consecutive $x$ coordinates in ECC?

From my basic understanding not all values of $x$ coordinates can satisfy a given elliptic curve equation, i.e. some $x$ coordinate values are not valid points on the curve because $x^3+ax+b$ is not a ...
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0answers
71 views

Is there any pattern in points on EC?

I read some where in crypto.stackexchange answer (related to EC-SRP protocol) that there is pattern in points on elliptic curves, i.e. if given some points containing mix of correct and wrong points ...
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1answer
111 views

Is only one shared secret generated by ECDH per key pair?

I'm confused about ECDH. Using their public keys and private keys, two entities can arrive on a shared secret. But from the equations I've seen, it looks like ONLY the numbers present in their key ...
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1answer
88 views

What aspect of elliptic curve encryption paradigms makes them especially susceptible to quantum based attack algorithms?

This was a statement made during a talk at today's DFN-CERT conference but unfortunately it wasn't explained further. Can anyone shed light on why elliptic curves are susceptible to quantum based ...
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1answer
151 views

How does ECDHE_RSA key exchange mechanism work?

Using Wireshark, I found these data exchanged with google.com over TLS: Client Hello possible cipher suites and possible curve types (eg. secp256r1) sent Server Hello cipher suite selected ...
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3answers
26k views

How can I use SSL/TLS with Perfect Forward Secrecy?

I'm new to the field of cryptography, but I want to make the web a better web by setting up the sites that I host with Perfect Forward Secrecy. I have a list of questions regarding the setup of ...
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0answers
90 views

How can ECDSA signatures be shortened (to be used as a product key)?

So I made my own serial key generation software, using ECDSA, for use in my own applications and it works great so far! To keep the serial key short enough I use a 128 bit EC curve. My final signature ...
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2answers
71 views

What does variable-base point/scalar multiplication mean in ECC?

I am a bit confuse about the term, variable-base point/scalar multiplication, in Elliptic Curve Cryptography. What I have understood so far. It means that the base or point on EC is variable/unknown. ...
2
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1answer
91 views

Parameters for elliptic curve prime192v3

I'm looking all over the internet for prime192v3's parameters. I think I may have found them here, but it doesn't say what variable each number matches to. Is there some central place where I can find ...
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1answer
388 views

Safe elliptic curve point addition using projective coordinates: How do I tell if the points are the same?

I am trying to implement elliptic curve point addition in hardware for NIST p256 and p384 curves. I have noticed the following issue with the suggested NIST routines: Consider routine 2.2.7 of ...
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1answer
104 views

Koblitz encoding a message to a point, what is the “associated auxiliary base parameter”?

I am looking at the Koblitz method for encoding a message as an elliptic curve point. The first step given in the paper I'm reading is: "Choose an elliptic curve and its associated auxiliary base ...
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1answer
246 views

Creating serial key generator using ECDSA, how to get signature short enough?

I've written some questions in this stackoverflow and got great responses but now I'm trying to wrap it all together. I have for the last couple of weeks been building a serial key generator project ...
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51 views

Are there any asymmetric composite order group bilinear pairings?

Are there any asymmetric composite order group bilinear pairings? Is there a drawback of asymmetric over symmetric bilinear pairings of composite order either in efficiency or in security ?
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1answer
49 views

In a additive group is it hard to calculate $bg$ given $ag, g, abg$

The ECDH problem defined that given $g,ag,bg$ it is difficult to calculate $abg$. But it is also difficult to calculate $bg$ given $ag,g,abg$. where $g$ is generator and a,b are elements of group.
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1answer
90 views

What are the computational benefits of primes close to the power of 2?

Recently I was reading some article about the Bernstein's Curve25519. This is a particular Montgomery curve over $\mathbb{F}_q$ where $q = {2^{255}-19}$. What I missed or was unable to understand is ...
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1answer
249 views

Is cryptanalysis of CTB-Locker really impossible?

It seems that CTB-Locker make a lot of victims nowadays, and yet, the full encryption scheme of it is now publicly known [1,2]. Would any of you could find a weakness to exploit in this encryption ...
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186 views

ECC considered secure in OpenSSL?

this is my first question, please bear with me if it comes across silly. If I openssl ecparam -list_curves on my OpenSSL version (1.0.1f), it spits out the ...
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2answers
107 views

Explanation of each of the parameters used in ECC

I'm having a very difficult time finding a clear explanation of the parameters used elliptic curve cryptography. I know for certain that $p$ is the number or order or whatever of the given field that ...
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2answers
138 views

Why does NaCL have different keys for signing and encryption?

I want to start using NaCL to sign messages that will go into a message queue, and I noticed that it generates different keys for each operation. Is there a reason for this? Can I not use the same PK ...
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2answers
140 views

In ECC, how do I prove that point addition is commutative?

I am studying elliptic curve cryptography and this question is related to the commutative property of point addition operation. Point addition $P_3(x_3,y_3)$ of two points $P_1(x_1, y_1)$ and ...
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2answers
145 views

Why are some $x$ coordinates unsuitable for an ECDSA generator point?

For Bitcoin's ECDSA curve (secp256k1, where $a=0$, $b=7$), why can't the generator point's first coordinate be $x=0$? That is, the point on the curve would be $(0,y)$ where $y$ satisfies $y^2 = 0^3 + ...
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1answer
51 views

How do you derive the lambda and beta values for endomorphism on the secp256k1 curve?

You can see a little background about this on this bitcointalk post by the late Hal Finney. $\beta$ and $\lambda$ are the values on the secp256k1 curve such that: $$\begin{align} \lambda^3 &= 1 ...
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273 views

Elliptic Curve based blind signature implementation

I want to use Elliptic Curve based blind signature scheme for my research. There is no proper implementation of ECC-based blind signatures. Can someone describe to me which things I need to follow ...
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187 views

Is there a flaw in this ECC blind signature scheme?

Recently I've found the following work on the internet: An ECC-Based Blind Signature Scheme The paper claims to be an ECDSA blind signature however it seems that their scheme has a flaw in it. The ...
4
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1answer
209 views

Isn't the security of EC curve 25519 126 bits?

The security of the EC25519 is given as 128 bits, but since the order of the group is 252 bits shouldn't the security be 126 bits? Given as half the magnitude of the underlying field, since DLP ...
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1answer
249 views

curve25519 weak points for contributory behaviour

The Diffie-Hellman on curve25519 is usually calculated using the base point $(9,…)$ which induces a cyclic subgroup of $G:=\{\infty\}\cup(E(F_{p^2})\cap(F_p\times F_p))$ with index 8, i.e. there is a ...
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2answers
145 views

What is a good way to demonstrate elliptic curve cryptography?

For school (high school) I am writing an essay on elliptic curve cryptography. The assignment needs to include a practical part, so I decided to write a Python class for elliptic curves. This class is ...
2
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2answers
437 views

How do I convert the definition of E-521 into a curve definition a la Bouncy Castle?

I am currently trying to create an ECCCurve for E-521. Unfortunately, it is not currently a named curve in the library I am using, so I will have to define it manually. I am using the definition of ...
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2answers
2k views

Are there any Secp256k1 ECDSA test examples available?

Are there any available test cases for testing elliptic curves like secp256k1 (Korblitz curves from http://www.secg.org/collateral/sec2_final.pdf)? For curves like P192 there are for example those ...
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1answer
120 views

C# implementation of curve25519 to ed25519 conversions [closed]

WRT the selected answer here: Can curve25519 keys be used with ed25519 keys? Is there any c# implementation of this or equivalent? Thanks.
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2answers
278 views

Solving Quadratic equations in Galois Field (2^163)

Hello I am working on implementing a message to elliptic curve point mapping hardware circuit I have done some research and found out the koblitz mapping method: I will be using a field of binary ...
3
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2answers
178 views

Which multiplicatively homomorphic encryption scheme supports encryption of 0?

I want a multiplicatively homomorphic encryption scheme that supports encryption of 0 (e.g. Elgamal doesn't support). I also want the multiplication to be operated on the ciphertext of 0, i.e., if ...
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1answer
118 views

Polynomial division hardware implementation

I am beginning the implementation of the polynomial binary division algorithm now as I understood i will be checking the MSB bit if 1 to XOR and shift the sum if 0 i will only shift. What I am not ...
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1answer
193 views

Can keys from Bitcoin's Hierarchical Deterministic Wallets be correlated (reducing privacy)?

I'm trying to understand if the feature "Hierarchical Deterministic Wallets" in Bitcoin allows for complete privacy of all derived keys, and if any of those keys can be associated with each other ...
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131 views

How represent message in Menezes–Vanstone elliptic curve cryptography

I ask about represent message in Menezes–Vanstone elliptic curve cryptography I now encrypt function as follow $C_1 = (M_1 * K_1) mod\ P$ $C_2=(M2 * k_2) mod\ P$ My question is about how much the ...
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65 views

request for data to test deterministic ecdsa signature algorithm for secp256k1

I’m implementing the RFC 6979 procedure to compute a message signature. I want to test my program on the secp256k1 elliptic curve. Note the “k” in secp256k1, i.e. the Koblitz curve. If you have the ...
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83 views

processing time for multiplication and exponentiation in pairing base cryptography

I'm using the Boneh-Boyen-Shacham signature scheme and want to estimate complexity in my scheme. As reported in "Scott M., Efficient Implementation of Cryptographic pairings", if we set parameters ...