Questions tagged [elliptic-curves]

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 consider more specific tags such as discrete-logarithm and ecdsa.

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318 views

Can you tell me why doing scalar multiplication of a point on a Elliptic curve over a finite field gets to a point at infinity?

I am reading Programming Bitcoin. The author said: Another property of scalar multiplication is that at a certain multiple, we get to the point at infinity (remember, the point at infinity is the ...
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1answer
223 views

Why is encryption slower than decryption in elliptic curve cryptography (ECC)?

While performing encryption using public key and decryption using the private key, I am always finding that encryption takes more time than decryption in elliptic curve cryptography (ECC). It's the ...
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54 views

Book request about elliptic curves, RSA and DSA

I understand that this question can be hardly downvoted, but so be it if someone gives me really useful references :) I wanna learn difference (deeply) between RSA, DSA, and ECC, especially I am ...
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226 views

What are the inverse operations in elliptic curve cryptography?

Public-private key cryptography is based on inverse operations that use separate input. In elliptic curve cryptography, what are those inverse operations?
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Explanation of Gallant-Lambert-Vanstone method / Endomorphism speedups [duplicate]

Can someone explain how the Gallant-Lambert-Vanstone method works (or which literature explains it)? It is also unclear to me how the Frobenius endomorphism can be used in some cases for a speedup. ...
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1answer
136 views

Are there shortcuts for computing ECC Point multiplication?

I'm trying to learn about elliptic curve cryptography. Let's say you have point $P$ and 256 bit number $n$ and you want to compute $nP$. It sounds like computing additions one at a time is not ...
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1answer
123 views

How to multiply two Public Keys in Elliptic Curve in Go

I am working on a messaging client similar to Signal. I am stuck on implementing Tripartite Diffie-Hellman handshake in which three DH exchanges are combined to authenticate both parties and produce ...
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2answers
1k views

Does secp256k1 have any known weaknesses?

I am wondering whether there are any properties of the curve which would technically make it easier to attack than any other curves of 256 bits in size. I have heard that being a Koblitz curve, it ...
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1answer
54 views

Why public key has two parts in my secure messaging client similar to signal

I am working on a Golang code similar to Signal protocol. I need to modify it. I am confused on tripartite Diffie-Hellman handshake part of code, i.e. why public key has two separate parts as compared ...
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1answer
213 views

ECDSA signing process

I am trying to learn how ECDSA works. I do not have a background in maths, but have been following a guide which has built me up from finite fields, elliptic curves. I am unable to figure out how a ...
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1answer
141 views

Why is it better to add and double points on an elliptic curve using projective space?

I have been given a textbook which defines the addition of two points on an elliptic curve and the doubling of a point on an elliptic curve. This textbook explains elliptic curves in projective space ...
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1answer
190 views

Convert affine to projective coordinates and vice versa in ECC?

I am working on a small project. An elliptic curve equation with y^2=x^3-3x+27 mod 43, a point $Q=(1,38)$, using point doubling method https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#...
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Curve25519 over Ed25519 for key exchange? Why?

I've been reading up on the Signal Protocol (in this PDF) and it seems to be using Curve25519 for ECDH and EdDSA (with Ed25519) for signatures. My question is why not use only Ed25519? This ...
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How is EC key encoded in PKCS#8?

I just started working with certificates and signatures. For an application I write I need a key pair for ECDSA signatures, using the elliptic curve secp384r1 (aka NIST P-384). I produced such a key ...
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1answer
248 views

How can I exploit the structure of the secp256k1 prime for fast arithmetic?

I'm implementing logic on an FPGA (programmable chip) that does the key verification part of ECDSA on the curve secpk256k1, in which all operations are mod p where $p = 2^{256} - 2^{32} - 2^9 - 2^8 - ...
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199 views

Curve25519's Y coordinate of Basepoint origin

The paper High-speed high-security signatures by Bernstein et al. introduces the Edwards curve Ed25519. Concerning the base point $B$, it says that $B$ is the unique point $(x,4/5)∈E$ for which $x$...
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Isogeny of elliptic curve

If we have two elliptic curves $E$ and $E'$ and the points of both elliptic curves are same. Then all the points of $E$ map to all the points of another elliptic curve $E'$. For example $E$ has ...
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39 views

How does the order of a group, it's torsion subgroup and the co-factor link?

Given an elliptic curve that defines some group of non-prime order, with co-factor h. Would it then have a h-torsion subgroup? What are the implications for ECC ...
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Deterministic generation of RSA keys for IPFS / OrbitDB [duplicate]

I am in the process of working on a decentralized application using IPFS and OrbitDB. IPFS uses 2048 bit RSA keys for the Node runtime peer-id and secp256k1 for read/write access in OrbitDB. For ...
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364 views

Difference on montgomery curve equation between EFD and RFC7748

There is a subtle difference between the 2 implementations for a Montgomery curve defined from the 2 following links https://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html A = X2+Z2 AA = ...
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730 views

Can Shamir’s Trick crack the cryptographic strength of ECDSA?

Recently stumbled upon a discussion in the forum What is Shamir’s Trick used for? Are there any such examples?
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48 views

Elliptic curves - operations in larger groups - performance

According to my measurements and to this work, it seems that operations, for example scalar multiplication, are more expensive in larger groups. If I have, for example, an 80-bit elliptic curve and an ...
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221 views

Why doesn't the formula work when checking two ECDSA signatures?

There are two generated ECDSA signatures X - Private key S = ((Z + (X * R)) / K) mod n S` = ((Z` + (X * R`)) / K`) mod n G - Base point, of order n; ...
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451 views

Which hash is used when providing signature algorithm ED25519 or ED448?

From TLS 1.3 there are two signature algorithms using edDSA: /* EdDSA algorithms */ ed25519(0x0807), ed448(0x0808), All the other signature-...
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ECDSA - why is the first part of the signature used in the second?

Using the terminology of https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm Why is the second part of the ECDSA signature defined as: $s = k^{-1}(z+rd_A)\text{ mod n}$ ...
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53 views

Why doesn't the JOSE suite/JWA include ECIES?

The JOSE suite specifics use of RSA-OAEP (for when one party has an RSA key) and ECDH (for when two parties have EC keys) in JWA. Why doesn't it include ECIES? It seems like a way to derive a key ...
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ECC How do the Curve, its number of bits of security and key size affect the maximum size of ciphertext?

First of all, excuse me if this question is too noobish. I'm trying to understand how these things are relate: Curve type, its 'number of bits of security', size of the key and the maximum ciphertext ...
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1answer
218 views

Secure multi-party computation for digital signature

Is there any practical algorithm that will allow to use public key cryptography (RSA or ECC) in the following way There are N parties. Up to M are malicious adversaries (were trusted, but got taken ...
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1answer
76 views

Subtracting one pederssen commitment from another

I am building a range proof to prove that a secret number x lies between a specific range a prover commits to a values a<x<b prover generates a pedersen ...
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1answer
246 views

The Secp256k1 curve is used in cryptocurrency. Can someone generate a private key with a different curve?

Many cryptocurrencies use Secp256k1. Every cryptocurrency library comes with its own redundant implementation of Secp256k1, ECDSA, RIPEMD160, and SHA256. So, there can be some inconsistencies across ...
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EC non-shared cryptosystems - different group for every party

Efficient Identity Based Parameter Selection for Elliptic Curve Cryptosystems by Arjen K. Lenstra contains a proposal for a non-shared elliptic curve cryptosystem. Every party chooses its own field ...
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1answer
84 views

Does Proxy re-encryption can re-encrypt large data?

Many resources talk about the benefit of Proxy Re-encryption (PRE) and I also implement my PRE using Elliptic Curve key pair. But after I set up Global parameters, I can encrypt very small data maybe ...
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1answer
143 views

Generating a key pair using a signature generated by an existing key

I’ve built an app in which each user has a private/public key pair and I want to generate a second one for them, however I cannot store the second private key anywhere. What would be the drawbacks ...
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Reason for including the public key of the key agreement in the KDF

I found the following text when looking up KDFs: In comparison, the so-called DHAES mode in IEEE 1363a mandates to use the binary representation of the sender’s public key as an input parameter. ...
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1answer
104 views

Generating a small EDDSA curve

I have an application that would benefit from very small (e.g. 16-20 byte) EDDSA keys and small signatures. It's an application where the goal is more to deter DOS attacks than "hard" security, so ...
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72 views

Equivalence of cryptographic problems

Are integer factorization, discrete log and ECDH problems equivalent? I know that factorization and discrete log are equivalent but are one of those two problem equivalent with ECDH? Cand someone ...
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3answers
219 views

Is RSA in decline across the board?

From what I gather from the internet (source), the recommended practice for 2019 and beyond is to avoid RSA and use ECDH and ECDSA. Is this the general case?
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1answer
182 views

Is it important to defend against key substitution attack in ECDSA?

When planning a file signature scheme (basically, just to sign all files content). Is it obligatory to defend against ECDSA key substitution attack? ISO/IEC 14888-3:2018 NOTE 5 states: The ...
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1answer
54 views

Elliptical Curve Actual Encryption

Im havirng a had time understanding ECC. For example, I have the equation below: ...
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802 views

How can you derive a P-256 public key from the X and Y points

Deriving a secp256k1 public key is also possible. For whatever reason, I'm only being provided X and Y, not the public portion. I just need to get the binary representation of the public key given ...
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3answers
734 views

Pedersen commitment in elliptic curves

I try to understand Pedersen commitment in elliptic curves over finite fields. I could use some clarification. Let's say we have two generators $G$ and $H$. Is that required that $G$ and $H$ are ...
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93 views

Precomputation attacks against ECDH

Diffie-Hellman groups are vulnerable to sieving precomputation attacks. These attacks allow a one-time computation against a given DH modulus that makes it practical to attack all subsequent key ...
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1answer
196 views

What is this EC key derivation method called?

I'm looking to identify the EC key derivation method used in Hyperledger Fabric. I can't find anything in the docs or the protocol specs, but the functions' code is here for the private key and the ...
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2answers
756 views

What motivated the creation of RSA and ECDH?

Recently I've been learning about cryptography and so far I am loving it. However, there are some things I do not comprehend. As far as I know, RSA was published in 1979 while New Directions on ...
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769 views

Is it possible to derive a public key from another public key without knowing a private key (Ed25519)?

I have a following use case: User has his master public (sk) - private (pk) key pair (Ed25519). In DB we store a public key. Is ...
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Patterns in elliptic curve division polynomials

While looking at division polynomials of elliptic curves in relation to this and this questions, I noticed some patterns. I am wondering if anyone knows of general formulas the describe these patterns....
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EC-ELGAMAL message mapping

I have been able properly set up an EC-elgamal protocol by using algorithms available in an IP that I have developed. Everything works fine, except for the fact that I haven't been able to completely "...
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1answer
187 views

Can specific Weierstrass curves be some benefit from Montgomery/Edward form?

I have noticed that DBL/diffadd in Edward/Montgomery form almost double fast than Weierstrass form(EFD), and curve25519 is empressive high-performance.The transformation between these forms can be ...
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ECC - complex multiplication and key agreement

I'd like to ask three questions - 2 of them regard CM method. The last is regarding the ECC domain parameters generation on the fly, see https://eprint.iacr.org/2015/647.pdf What role has ...
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Differential representation of binary curve as a public key

Given elliptic curve $E$ over binary field $k$, a public key is the pair $(x,y)$ in $E$ and $x$ and $y$ in $k$. The differential representation of $(x,y)$ is $w = x + y$. What security implications ...

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