The difference between compressed and uncompressed

[semaforo]

  Hello,

  I'm trying to learn how to use brain wallets and wondering what the difference is between compressed and uncompressed. I notice that the tool at brainwallet.org offers support for compressed wallets, but I don't see such an option at bitaddress.org .

   I wanted to make a compressed wallet because I've heard they have better security, but I can't find any way to use brainwallet.org tool offline.

    I imagine the security difference isn't that huge, but I am still just wondering if someone can teach me about what the difference is.

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[jackjack]

Let's take a private key: 000...0001
The corresponding point on secp256k1 is :
X = 79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
Y = 483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8

The corresponding public keys are the two ways of serializing the point above:
Compressed: 0279BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
Uncompressed: 0479BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798483ADA7726A3C 4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8

As you should know, address=hash160(public key)
So this gives two addresses:
Compressed: 1BgGZ9tcN4rm9KBzDn7KprQz87SZ26SAMH
Uncompressed: 1EHNa6Q4Jz2uvNExL497mE43ikXhwF6kZm

[Abdussamad]

^^ Yeah we all think in hexadecimal EC math and understand all that perfectly.

[jackjack]

I'd really like to know how you can explain the difference differently

Btw OP, absolutely same security for both

[Abdussamad]

Well let's see now:

   I wanted to make a compressed wallet because I've heard they have better security, but I can't find any way to use brainwallet.org tool offline.

    I imagine the security difference isn't that huge, but I am still just wondering if someone can teach me about what the difference is.

This answer is easy to understand:

http://bitcoin.stackexchange.com/a/3062

[Abdussamad]

Also to use brainwallet.org offline just visit the site and save the page to your hard disk. Then whenever you want to generate an address you can open the page you saved without needing to go online.

[deepceleron]

Instead of an elliptic curve, imagine the curve of this river:



I can describe a position on the river between mile 0 and mile 7 by using both X and Y coordinates, much like a private key describes an X and Y coordinate on the elliptical curve.

You will see however that if I only tell you the X coordinate, you can still figure out where on the river you are. This would be the "compressed" river coordinate, telling it to someone would take half as much data.