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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What happens if no final subtraction is done in Montgomery multiplication?

I'm doing Montgomery arithmetic modulo $N = 2^{255}-19$ for the Curve25519, picking $R = 2^{256}$ for Montgomery. After multiplying two numbers $0 \leq A,B < N$ in the Montgomery representation ...
4
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1answer
84 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 ...
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0answers
49 views

What is th purpose of m and q in elliptic curve cryptography protocols?

In crypto protocols that contains calculus on elliptic curves I can often see $\dfrac{m}{q}$$Q$ where $m$ stands for order of EC points group and $q$ is the order of corresponding subgroup of $m$. $Q ...
2
votes
1answer
222 views

Simple digital signature example that one could compute without a computer?

I am working on a document to explain Bitcoin to students. But I am having a hard time translating the principle described in §2 of the Bitcoin whitepaper in layman's terms. There is a great question ...
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24 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 ...
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1answer
49 views

Could someone explain the given algorithm?

The following snapshot of the algorithm is taken from the book Guide to Elliptic Curve Cryptography published by Springer 2004. I don't understand that why at the statement 9.1 if both $T_1$ and ...
5
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2answers
869 views

Understanding elliptic curve encryption [closed]

I'm having a hard time understanding the elliptic curve encryption. One thing thing I don't understand is listing all the points on the curve mod p. Suppose I have the following elliptic curve: $y^2 = ...
0
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0answers
54 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 ...
3
votes
0answers
29 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 ...
5
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1answer
175 views

Finding the subgroup in isogeny-based cryptography

Isogeny-based cryptography is one of the newest post-quantum cryptography. Hardness of this system is based on finding isogeny between two elliptic curves. Also this is theorem: Elliptic curves ...
1
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1answer
37 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 ...
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0answers
24 views

Pairing on BN curves, GMP code

Is it possible to write a small implementation of tate pairing using BN curves using GMP. It does not need to be efficient. I just want to understand the steps. Thank you.
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2answers
92 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
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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?
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2answers
48 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
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2answers
75 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? ...
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1answer
48 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 ...
5
votes
0answers
53 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 ...
3
votes
2answers
555 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 ...
0
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0answers
33 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
30 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
1answer
55 views

Comparison Affine Coordinates and Projective Coordinates Addition in Excel

Kurve : EC : $y^2=x^3 + x + 1$ Generator:$(1,7)$ $p=23$ Result in Affine use Excel: $P=(1,7)$, $Q=(7,11) \implies P+Q=(18,20)$ Result in Projective use Excel: $P=(1:7:1), Q=(7:11:1) \implies ...
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2answers
73 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 ...
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2answers
42 views
3
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1answer
19 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 ...
3
votes
1answer
68 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 ...
39
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5answers
15k views

Who uses Dual_EC_DRBG?

Recent news articles have suggested that the NSA may be involved in trying to influence the cryptography in public standards or commercially deployed software, to enable the NSA to decrypt the ...
17
votes
1answer
6k views

ECDSA vs ECIES vs ECDH

Recently I started studying Elliptic Curve Cryptography and I just loved it. I want to transfer some big data (like 3KB), What is the best method, ECDSA, ECIES, or ECDH (and why)? I am confused, how ...
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votes
2answers
50 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 ...
2
votes
0answers
104 views

RSA_DH vs ECDH implementation

In ECDH protocol is possible, naturally, to use the same algorithm for calculate a secret key for both communication parties (Alice and Bob for example). It is possible to design also a same algorithm ...
5
votes
1answer
118 views

Which attacks are possible against raw/textbook elliptic curve?

A quick question, we know that raw RSA is a no go. To solve this we have different PKCS standards forcing structure on the input messages. For EC the story is something else. For signatures we have ...
2
votes
1answer
84 views

Is there an asymmetric algorithm that can perform double encryption?

I'm looking for any asymmetric algorithm can perform the serial encryption, by serial I mean double or more encryption with different key(same key size). RSA can not do it since the cipher of the ...
4
votes
2answers
308 views

Using Lattice-based cryptography for TLS\SSL

Given the general benefits of Lattice-based cryptography, such as: Post quantum Security Security from worst case scenario Efficiency What could the outlook of shifting from RSA \ ECC-based ...
3
votes
1answer
61 views

Why inversion and multiplication operations are costly in elliptic curves?

There are several algorithms for efficient scalar multiplication of an arbitrary point P(x,y) by some positive integer k in elliptic curves defined over $F_{p}$ or $F_{2^{m}}$. The scalar ...
1
vote
3answers
107 views

ECDH-ECDSA Combination

I am doing research on cryptography primitives at a basic level and I faced a question on encryption methods. I understood that ECDH is an approach to for secure key exchange between two parties ...
6
votes
1answer
95 views

Encoding scalar values to points on Ed25519

I'm interested exploring key derivation and threshold signature protocol that require point arithmetic (addition) on the private scalar values and $S$ values of the signatures in ed25519. ...
1
vote
1answer
38 views

Non-Degeneracy of the Weil pairing

In this YouTube video, Dan Boneh mentions that if both points are defined on the base field then the pairing is degenerate. Why is that? And specifically is this true if I use the Weil Pairing?
4
votes
1answer
157 views

great discovery in the field of elliptic curves cryptography?

Prof. Adi Shamir says in The Cryptographers' Panel 2016: i think that NSA has made a great discovery in the field of elliptic curves cryptography and NSA wants to avoid the increased use and ...
3
votes
3answers
175 views

Supersingular Isogeny Key Exchange broken?

Found this report detailing a quantum algorithm for computing isogenies between supersingular elliptic curves. http://cacr.uwaterloo.ca/techreports/2014/cacr2014-24.pdf with the quote ...
2
votes
1answer
94 views

Elliptic curve ElGamal with homomorphic mapping

I am interested in ElGamal due to the fact that you can achieve some degree of homomorphic properties. I became interested in applying ElGamal to elliptic curves, and found this other question with an ...
3
votes
2answers
253 views

Is there any reason to use RSA or DSA when we have ECC?

I am having trouble coming up with a use case for RSA or DSA. It appears that ECC is better in every way. Is this true? I am looking for cases where RSA/DSA is superior to ECC, not where it is used ...
0
votes
2answers
58 views

Named Elliptical Curve parameters

Are named curve parameters always the same? I know this may be a stupid question however I think this is the case. For example the secp256r1 is defined in this documet ...
3
votes
1answer
84 views

Why do the subexponential algoriths for the DLP not work for the ECDLP?

Elliptic curve cryptography is much more secure for the same parameters because attacks that work on the DLP do not work on the ECDLP. Why do the attacks fail in the latter case?
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1answer
28 views

How do we calculate DHKey using A's public key and B's private key?

I have 2 set of public/private keys. I would like to know how I can calculate DHKey. e.g: ...
1
vote
1answer
53 views

Shouldn't a signature using ECDSA be exactly 96 bytes, not 102 or 103?

Attempting to use openssl to create a signature is confusing on several levels: If I'm using it to sign a hash that I've already created (HMAC-SHA-384-192, specifically), a. why must I specify ...
4
votes
1answer
453 views

Curve25519 vs “Million Dollar Curve”

Quoting from the Million Dollar Curve website: By using publicly verifiable randomness produced in February 2016 by many national lotteries from all around the world, we propose to generate a ...
0
votes
2answers
115 views

Determine if a public key point y is negative or positive, odd or even?

Take an elliptic curve cryptography public key (x, y) and its additive inverse (x, -y). How do you identify which is the positive point and which is the negative point? Examples: Private key 1 -> ...
0
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1answer
56 views

Is there an additive homomorphic encryption that supports exponentation

For example say we have two numbers a and b. Now is there any partial homomorphic encryption scheme that allows to compute (a-b)^2 over the ciphertexts of a and b without round trips.
2
votes
3answers
330 views

Is there a 1:1 mapping between private and public EC keys?

After asking: Are all possible EC private keys valid? I learned that all 32 byte (256 bit) values greater than 0 and less than n are all valid private keys. This means that 99% of all 256 bit values ...