Elliptic curves are a mathematical structure. In cryptography, it is common to use the structure $y^2 = x^3 + ax^2 + b$ over a finite field. Questions relating to elliptic curves and derived algorithms should use this tag and might also consider specific tags such as discrete-logarithm and ecdsa.

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What are these twist attacks with cost $2^{58.4}$ on NIST P-224 curve, and when do they apply?

This page on Twist security mentions a combined attack and a twist rho attack, applicable in particular to NIST P-224 curve with cost $2^{58.4}$ something, with no mention precise definition of ...
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43 views

DLOG in $\mathbb{F}_{p^n}^*$?

Assume that we are given an element $g\in \mathbb{F}_{p^n}^*$ and $g$ does not belong to any of the smaller subfields contained in $\mathbb{F}_{p^n}$. If the degree of $g$ is some number $q$, how much ...
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139 views

Understanding Twist Security with respect to short Weierstrass curves

I'm trying to understand the "Invalid-curve attacks against ladders" section of SafeCurves Twist Security page and I have difficulties to apply it to short Weierstrass curves. That section claims ...
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26 views

Elliptic Curves Readdition

I found the term re-addition in https://www.hyperelliptic.org/EFD/g1p/auto-shortw-projective.html and I cannot figure out what it is. It has actually same complexity of addition and I dont see the ...
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224 views

Why does openssl use SHA1 in ECC when I use secp384r1 curve

I need a small clarification that why openssl using SHA1 in ECC when I am using secp384r1 curve, but in rfc they are saying we should use SHA2. Thing here is am using nanoECC in my DTLS, nanoECC ...
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1answer
97 views

What can be learned from the ciphertext of LibSodium's crypto_box_detached()?

LibSodium, (https://github.com/jedisct1/libsodium), has a function crypto_box_detached() which does authenticated encryption using the public key of the recipient ...
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1answer
91 views

How can convert affine to Jacobian coordinates?

I have a point in affine coordinates: $(x,y)$. What should I do when I want to convert to $(X,Y,Z)$ in Jacobian coordinates? I need it for calculating ECC in a prime field.
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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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102 views

becoming a cryptographer after math studies [duplicate]

After studying philosophy and being a philosophy teacher, I took back studies 4 years ago and I did a bachelor in maths. I'm in maths grad school now (I'm 32), and I would like to work in ...
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78 views

Which mathematical operations does secp256k1 point multiplication use?

To convert a bitcoin private key to a public key, the secp256k1 point multiplication math is used. Could I – theoretically – convert a private key to a public key just using the four arithmetic ...
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90 views

Protection of Elliptic Curve Implementations against side-channel attacks [closed]

Recent fast elliptic curve implementations, for example a presentation at Eurocrypt 2014 (earlier presentation slides, the paper) talks about protection against only timing attacks. Why only timing ...
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63 views

initiate the elliptic curve

when we consider a curve in a prime field for example Weierstrass form and want to initiate it in Miracl,we should give these inputs for initiate curve: ebrick_init(&binst,x,y,a,b,n,window,nb) ...
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3answers
130 views

Elliptic curve parameters

What's the meaning of 160 bit Curve in Elliptic curve ? or 192 or 224 or 256 and etc. And What is the standard for selecting this number of bit ? why they don't say 100 bit curve?
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71 views

advantages of hashing over elliptic curve signatures for a proof of work protocol

I'm trying to create a proof-of-work protocol for a proof-of-concept software, and it's basically something like this: ...
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1answer
149 views

What is the difference between “secp…” and “sect…”?

The National Institute of Standards and Technology (NIST) recommended elliptic curve domain parameters to have names such as “secp…” and “sect…”. For example: “secp224k1” and “sect571k1”. What is ...
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158 views

Why are we not using multiple ciphers per message?

I am aware of at least rsa, elgamal-encryption, and variations of elliptic-curves relying on different problems and that those problems are considered hard. However, if someone figures out a way to ...
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103 views

What is the (uncompressed) x,y-representation of a curve point on the P-256 NIST elliptic curve?

I am trying to understand the FIDO U2F Raw Message Format, especially the format in which a user public key should be provided. The documentation says the following: A user public key [65 bytes]. ...
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1answer
142 views

Bouncy Castle elliptic curve from explicit parameters (E-521)

I'd like to use a curve that's not included in the Bouncy Castle EC named curves spec, specifically E-521. According to the BC javadocs, you need a few values in order to do this: q, a, and b for the ...
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1answer
58 views

Is elliptic curve point multiplication semantically secure?

Is elliptic curve point multiplication semantically secure? I'd like to know if there are some sets of elliptic curve parameters (e.g. NIST curves) that are proved to be semantically secure or that ...
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1k views

Why do the elliptic curves recommended by NIST use 521 bits rather than 512?

Wikipedia says in reference to the elliptic curves officially recommended by NIST in FIPS 186-3: Five prime fields for certain primes p of sizes 192, 224, 256, 384, and 521 bits. For each of the ...
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2answers
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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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1answer
230 views

Why is 224 bit ecdsa faster than 192 bit ecdsa?

I ran several benchmarks using openssl on 2 different computers and I got a surprising result. for the Nist 192 bit curve the benchmark result is ...
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1answer
56 views

How can i calculate prime of Elliptic Curve?

In many articles i have found directly the calculation of prime elliptic curve. How can i calculate this prime $p$ ? For example if I consider NIST P-256, $ p = 2^{256}-2^{224}+2^{192}+2^{96}-1$. Why ...
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1answer
119 views

Point addition equation in projective co ordinates

How can I get point addition equation for elliptic curves in projective co ordinate system? Can I get it by changing $$ x = X/Z $$ and $$ y =Y/Z $$ in the equation for affine co ordinates' group law? ...
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59 views

Scalar multiplication of elliptic curve point by a fraction

I'm implementing an algorithm that works on a generic finite cyclic group written in the classic multiplicative notation: (G,*) = < g > , n = |g| At a ...
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1answer
69 views

How to calculate kinv from the given k value

I am implementing an ECDSA NIST test vectors verification application. The test vectors are taken from http://csrc.nist.gov/groups/STM/cavp/#09. One of the test vectors is given below: ...
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43 views

Selecting a Bouncy Castle named curve for ECC [duplicate]

I have been tasked with implementing ECDSA and ECDH in Java using the Bouncy Castle library. However, I am unsure of what curve to use. I am aware of the named curves listed in BC, and I've done a ...
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How does one calculate the scalar multiplication on elliptic curves?

I found this example online: In the elliptic curve group defined by $$y^2 = x^3 + 9x + 17 \quad \text{over } \mathbb{F}_{23},$$ what is the discrete logarithm $k$ of $Q = (4,5)$ to the base ...
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1answer
485 views

Storage of Private Keys

I'm building a bitcoin web application that will require all users to be assigned a wallet for adding funds to their account. I plan on exposing the public key to the user (the bitcoin address). Users ...
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1answer
232 views

Can Secp 256 K1 curves “map” to a value on FIPS 186-3 or P-256?

I'm looking at Secp 256K1 vs UProve's FIPS 186-3 or P-256 implementation. Is there any relationship between the curves such that I can consistently "map" or "project" values from one curve to ...
4
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1answer
502 views

Families of public/private keys in elliptic curve cryptography

I'm looking for a related key scheme for elliptic curve cryptography. The basic idea would be that there would be a master public key and a master private key. From the master public key, you could ...
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2k views

Is secp256r1 more secure than secp256k1?

Curves secp256r1 and secp256k1 are both examples of two eliptic curves used in various asymmetric cryptography. Googling for these shows most of the top results are Bitcoin related. I've heard the ...
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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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35 views

ECIES: Purpose of optional shared information?

According to Wikipedia the ECIES algorithm has two optional shared information $S_1$ and $S_2$. They are used as follows: Generate a random shared secret $Z$ according to ECIES, which will never be ...
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1answer
65 views

ECIES: Purpose of MAC?

Assumptions: $A$ wants to communicate with $B$ $A$ knows a public key $P_B$ which is trusted by a third party and belongs to $B$ $A$ knows the address of someone who pretends to be $B$ $A$ wants ...
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37 views

Size of Messages Exchanged by PRV and VER for Schnorr Protocol

In this file Elliptic Curve Based Zero Knowledge Proofs and Their Applicability on Resource Constrained Devices I don't understand the Table 6 (Table 6: Size of Messages Exchanged by the Prover(PRV) ...
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2
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86 views

Prevent MITM attack while encrypting data by using ElGamal ECC?

I am using ElGamal ECC to encrypt my plain text data. I want to ensure that my data is safe from a Man-In-The-Middle attack. What methodology I can adopt to achieve this goal? How can we prevent a ...
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82 views

Type G Bilinear Pairings

I was reading PBC and its implementations for finding pairing parameters. I am particularly interested in implementing a BLS signature scheme with 20-byte (160-bit) signatures ("short signatures"). ...
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1answer
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Proving Non-Existence of ECC Backdoors

In light of the NIST Dual EC DRBG scandal, I was intrigued by a NIST slide (slide 9) that said the two points P and Q can be chosen so that the chooser can prove they don't have a backdoor. This ...
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111 views

RSA and ECDSA Certificate Sizes

Is there a table (or a whitepaper from official sources) that compares the size of X509 certificates generated with RSA (starting from 1024 bits) and ECDSA (starting from 160 bits) ? Thanks for the ...
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86 views

ECC cryptography with shorter signature when not needing high security?

I am new here and fairly new to cryptography, so if I say something wrong, let me know. I am trying to set up a system where a user can receive a temporary license key over the phone, put it into ...
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1answer
895 views

Is Curve25519-java secure?

I have only about 2 weeks of cryptography experience mostly in the form of questions on bitcoin.se. Is Curve25519-java up to date with current Curve25519 standards? Is Curve25519 itself secure? ...
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265 views

Rely on NSA Suite B Cryptography?

NSA's Suite B Cryptography suggests some cryptographic algorithms for encryption, digital signatures, message digests and key agreements. The selected algorithms and their key size are suggested by ...
2
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1answer
306 views

How do the following new (2013) ECC curves compare in security or efficiency? [closed]

I read about the following "safe" ECC curves and notably, secp256 and all the NIST curves are marked as "unsafe" when compared to more modern curves. I need a curve for signing or encryption, (or ...
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0answers
102 views

Hardware Implementation of Pairing over BN curves

I am in the middle of FPGA based Hardware architecture design for the computation of Pairing (particularly R-ate Pairing) over BN curves. Where, the point addition, and point doubling should be ...
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2answers
705 views

Converting Ed25519 public key to a Curve25519 public key

I understand that: $$x_{montgomery} = \frac{1 + y_{edwards}}{1 - y_{edwards}}$$ Using the libsodium ed25519 implementation, I have tried to write the following: ...
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96 views

Difference between “ECDH with cofactor key” and “ECDH without cofactor key”?

I need to use “ECDH with a cofactor key” for generating symmetric key. I have a fair idea on how ECDH works, but I don’t understand the cofactor part. What is the difference between ”ECDH with a ...
3
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2answers
633 views

Can curve25519 keys be used with ed25519 keys?

Can curve25519 keys be used with ed25519? I'd prefer to use ed25519, but there isn't a fast java version. For my application, I'd like to use curve25519 until I can get a faster ed25519 for java. ...
4
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1answer
174 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 ...