How is Elliptic Curve Cryptography Encryption Fast?

Today I learned about elliptic curve cryptography. And there is something I do not get. Probably I'm getting the basics wrong. But from what I understood, we are starting at one point G on the elliptic curve and then you multiply it with a. Finally you land on another point on the elliptic curve. And it is very hard to guess the factor a that brought you there. You can only figure this out by attempting (a=1, a=2, a=3, ...). But what I don't understand is that the whole encryption process is done the same way, meaning the encryption performance increases linearly with the size of a. So how is cracking the hash taking any longer than the encryption itself? π€¨

And I get that there are other constraints to this crypto system as the use of modulo. But I do not see how even this would change a lot on the issue I stated.

Now, I'm obviously dumb. I obviously do not understand something. I would just like someone to explain me what I get wrong :) Thank you very much in advance.

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The Elliptic Curve Cryptography Explained - HackTheBox Shrek youtube.com/watch?v=krfU8β¦
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Prerequisites for learning elliptic curve cryptography?

Hello, I am wondering how advanced the mathematics is for the practical application of elliptic curve cryptography. Can someone with a math undergraduate degree understand it and what type of prerequisite math is required?

Thank you

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(Very) Basic Intro to Elliptic Curve Cryptography qvault.io/2020/09/17/veryβ¦
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Implementing Curve25519/X25519: A Tutorial on Elliptic Curve Cryptography martin.kleppmann.com/papeβ¦
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New courses on distributed systems and elliptic curve cryptography (by Martin Kleppmann) martin.kleppmann.com/2020β¦
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elliptic gem - elliptic curve digital signature algorithm (ECDSA) cryptography with OpenSSL made easy / easier (incl. secp256k1 curve) github.com/rubycoco/blockβ¦
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New courses on distributed systems and elliptic curve cryptography (by Martin Kleppmann) martin.kleppmann.com/2020β¦
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New courses on distributed systems and elliptic curve cryptography (by Martin Kleppmann) martin.kleppmann.com/2020β¦
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Understanding Bitcoin Cryptography - Basics of Public Key Crypto/Elliptic Curves youtu.be/5JVVY8euZHU
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Day 5 - ecdsa Gem - Open Up 10,000,000,000 Accounts - Bank the Unbanked Using Elliptic Curve (EC) Cryptography and the Digital Signature Algorithm (DSA) - Be Your Own Bank @ Ruby Blockchain Week 2021 / 7 Days of Ruby (Crypto) Gems planetruby.github.io/gemsβ¦
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Understanding Bitcoin Cryptography - Basics of Public Key Crypto/Elliptic Curves youtu.be/5JVVY8euZHU
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New courses on distributed systems and elliptic curve cryptography (by Martin Kleppmann) martin.kleppmann.com/2020β¦
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sample math IAs one elliptic curve cryptography?

So im planning to do an IA on the ECC as im interested in cryptocurrency. Are there any sample IAs or good research papers i can refer to, as idk how to go about it that well. If anyone ahs done this topic any advice or reference material. Im in a bit of a hurry so any help is appreciated.

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New courses on distributed systems and elliptic curve cryptography martin.kleppmann.com/2020β¦
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Luks and elliptic-curve cryptography

Hello fellow crypto enthusiasts, I was wondering if there is any chance to get a luks encrypted filesystem by using ECDSA or something similar. I can not find this option in my cryptsetup benchmark and failed to find any further information on this. Is it even technically possible or sensible?

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Elliptic Curve Cryptography btcclj.com/posts-output/2β¦
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Elliptic Curve Cryptography in Clojure Part II

Hey guys, here's the second part of the elliptic curve cryptography article, which is part of the larger Programming Bitcoin in Clojure I am doing right now.

Let me know what you think! Constructive feedback is always welcome.

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How elliptic curve cryptography works in TLS 1.3 habr.com/en/company/qratoβ¦
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Learning fast elliptic-curve cryptography in JS paulmillr.com/posts/nobleβ¦
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Vitalik: "In a sea of coins based on elliptic curve cryptography, how does Bitcoin [Core] even plan to stick out? twitter.com/vitalikbuteriβ¦
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Can DNA computing break elliptic curve cryptography?

Iβm a newbie in cryptography, and doing some basic research on hash functions, RSA and elliptic curve cryptography, etc.

Iβm wondering if DNA computing can feasibly break elliptic curve cryptography with the current technology available? I found this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2292844/) in which the authors described a theoretical method based on DNA computing to solve elliptic curve logarithm problem. Their method is quoted as follows:

βconsider point P and Q are given, and l is what we want to get which matches Q = lP. First, we amplify P into two tubes and add P in one tube. Check if 2P equals to Q; if not, note down the value of 2P and pour two tubes together. Then, amplify the tube into two tubes and add 2P in one tube. Check if any point equals to Q; if not, note down the value of 4P and pour two tubes together, or we get the value of l. Then, amplify the tube into two tubes and add 4P in one tube,β¦, while this loop executes n times, the value from 1 to 2n for l will have been checked, and the elliptic curve cryptosystem has been broken by the solved elliptic curve discrete logarithm problem.β

Is this even remotely feasible with current technology? I know that the primary drawback of DNA computing is that it takes too much space - factoring a 10^3-bit number, for example, would require 10^20000 test tubes (https://www.semanticscholar.org/paper/Factoring%3A-The-DNA-Solution-Beaver/5e292a3100699187b1943b1dd65848fb46e855a5) using the Hamiltonian path idea proposed by Leonard Adelman.

Any thoughts?

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Introduction to Elliptic Curve Cryptography medium.com/@animeshgaitonβ¦
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ProtonMail now offers elliptic curve cryptography for advanced security and faster speeds protonmail.com/blog/ellipβ¦
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Why is elliptic curve cryptography with 256 bits considered to be safer than RSA if the key is smaller? Shouldnβt it be easier to brute force?
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Would appreciate opinions on this crypto code titled 'Image Encryption Using Elliptic Curve Cryptography.

https://github.com/vinaychawla11/Image-Encryption-Using-Elliptic-Curve-Cryptography-and-exchange-using-web-sockets

Here is the link to my final year project, Image Encryption Using Elliptic Curve Cryptography. It uses the ECIES(AES256 + ECDH key sharing) Since cryptography is a vast field, I would appreciate opinions and research ideas for the same.

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ProtonMail now offers elliptic curve cryptography for advanced security and faster speeds - ProtonMail Blog protonmail.com/blog/ellipβ¦
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How elliptic curve cryptography works in TLS 1.3 habr.com/en/company/qratoβ¦
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Ideas for a New Elliptic Curve Cryptography Library (2015) briansmith.org/GFp-0
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ELI5: How is Elliptic Curve Digital Signature (ECDSA) differ from Elliptic Curve Cryptography (ECC)?

ECC can be used to create digital signature, whereas the ECDSA use ECC to create digital signature. So how they are different in term of signing especially the performance? To be honest, i am doing a homework to compare ECC, ECDSA and some other algorithms.

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How elliptic curve cryptography works in TLS 1.3 habr.com/en/company/qratoβ¦
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Question about potential attack if elliptic curve cryptography were broken.

As I understand it, we use P2PKH instead of P2PK, so that if elliptic curve cryptography were broken there would still only be hashes of public keys present on the blockchain, which are way harder to break. If you spend an output however you have to provide the corresponding public key, as specified in the P2PKH locking script.

If elliptic curve cryptography were broken and someone were to send such a transaction, couldn't you just take that, find out the corresponding private key and then send a competing transaction with a higher fee to steal the money?

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Today's topic is Eliptic curve cryptography.

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week.

Experts in the topic are especially encouraged to contribute and participate in these threads.

Next week's topic will be Computational complexity.

These threads will be posted every Wednesday around 12pm UTC-5.

If you have any suggestions for a topic or you want to collaborate in some way in the upcoming threads, please send me a PM.

To kick things off, here is a very brief summary provided by wikipedia and myself with the help of my friend /u/t00random:

Suggested in the 1980's , elliptic curve cryptography is now a very succesful cryptographic approach which uses very deep results about algebraic geometry and algebraic number theory into its theory and implementation.

Exploiting the fact that elliptic curves have a group structure, it is possible to implement discrete-logarithm based algorithms in this context.

Further resources:

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π︎ Aug 16 2017
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Notes on Elliptic curves cryptography

When CTFs force you learn ECC. These are my notes and a dummy implementation in python for elliptic curve cryptography primitives which is kind of easy to use, not comprehensive though.

This can be used simply on the python prompt.

python cli

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How elliptic curve cryptography works in TLS 1.3 habr.com/en/company/qratoβ¦
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Elliptic Curve Cryptography in Clojure I

https://btcclj.com/posts-output/2020-06-18-elliptic-curve-cryptography-i/

The first part of the third section on my exploration of Programming Bitcoin by Jimmy Song but in Clojure.

Lemme know what you think!

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π︎ Jun 19 2020
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Why is elliptic curve cryptography with 256 bit key size considered to be more secure than RSA, if the key is smaller, shouldnβt it be easier to brute force?
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