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Sounds good. You are right about not being able to look up firstbits on a nonfunded account (what was I thinking?). That is why we have peer review, right?
1) Make the item with spots for two holograms and a final public key address
2) First party gets the item
3) Put the first private key in mini private key format under the first hologram
4) Ship the item along with the actual public key to the second party
5) Second party puts the second hologram on the item
6) Second private key in mini private key format under the second hologram
7) then adds the two public keys together, creating the final public key
9) From the final public key calculate the final public key address
10) This final public key adddress is etched/printed on the item somewhere, possibly on the hologram
11) The BTC funds are transmitted to the final public key address
At this point no one could possibly know the private key since it has never even been calculated.
To redeem:
1) Pull off both stickers
2) Get the two private keys
3) At a web site that supports the two key option, enter both private keys (Mt Gox, StrongCoin, etc. could be talked into supporting this option)
4) The web sites that support this option would then simply add the two private keys together
5) You now have the private key for the combined public key address etched/printed on the item
6) Redeem the BTC from the item
The other redemption options mentioned above are also possible.
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Here is my explaination from another thread:
1) Make the bar or paper bill with spots for two holograms and a final public key address
2) First party gets the item
3) Put the first private key in mini private key format under the first hologram
4) Put the firstbits of the public key address on the outside of the first hologram
5) Ship the item along with the actual public key to the second party
6) Second party puts the second hologram on the item
7) Second private key in mini private key format under the second hologram
8. Firstbits of the second public key address on the outside of the hologram
9) NOW the second party verifies the public key shipped with the item with the public key address on the first hologram
10) then adds the two public keys together, creating the final public key
11) From the final public key calculate the final public key address
12) This final public key adddress is etched/printed on the item.
13) The BTC funds are transmitted to the final public key address
At this point no one could possibly know the private key since it has never even been calculated.
To redeem:
1) Pull off both stickers
2) Get the two private keys
3) At a web site that supports the two key option, enter both private keys (Mt Gox, StrongCoin, etc. could be talked into supporting this option)
4) The web sites that support this option would then simply add the two private keys together
5) You now have the private key for the combined public key address etched/printed on the item
6) Redeem the BTC from the item
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Please hurry and ship mine to me before he finds out and asks you to stop  |
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What I really like about this idea is that ANYONE with access to a few BTC, the internet (to get to https://www.bitaddress.org) and a printer can do this. Very low tech and low cost. I have been giving away 1 BTC physical coins to friends and family and they cost almost 2 BTC each. For the cost of one coin I can give away 200 of these to total strangers (I am running out of friends and family that still want to hear about Bitcoins). |
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I would think a combination of the website and working phone app today would make physical Bitcoins able to replace cash tomorrow If you are going to dream then you might as well dream BIG I always say  |
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The www is not the issue, the issue is I told you mrcoin and it is mrcoins
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I can't believe that with all my yammerings all over this board that I have just now only cracked 200 posts. This makes me really appreciate the hard work and dedication of people like DeathAndTaxes who are over 2000!
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Hey Mike, you could even make coins with a sticker on each side. One from you and one from the insurance company. Put the final public key address on the second sticker with no public key address on the first one (so no one gets confused). That would be pretty cool. Logistical issues sure, but very cool. This thread and others like it is why I LOVE Bitcoins! BTW: this property can be extended to any number of "cosigners". Three stickers, four stickers, etc. etotheipi - Welcome to the party! I clicked on one of the links in your signature and all I can say is WOW. Everyone, if you liked this thread you will probably like his thread at https://bitcointalk.org/index.php?topic=29416.0 |
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Maybe one more thing:
Do you see/believe that for integers A, a, B, b, and G if A = a x G and B = b x G then
Z = A + B
= (a x G) + (b x G)
= (a + b) x (G)
where + is integer addition and x is integer multiplication?
Hopefully you know this to be true for integers, right? So now can you prove it?
Well it turns out this is also true for any finite field, for example the boolean field where A, a, B, b, G and Z can only be a 0 or a 1 and + is the boolean OR operation and x is the boolean AND operation.
You could prove this to yourself by trying every single possible combination of values for A, a, B, b, G where they can be either 0 or a 1.
Then the beauty of group theory is that if it is true for one finite field it is true for all finite fields.
The case in point is slightly different in that a and b come from a finite field and Z, A, B and G come from a finite (elliptical) group.
But asking for proof is like when I asked you for proof above. Do you see what I mean?
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Also, I think I have presented the simplest possible proof I can think of in post #32 and Mike presented proof by example in post #33. He wrote the code and did exactly what we are saying will work - and it worked. He took two actual private keys. Added them together and then computed the public key. He also took the two public keys and added them together and he got the same public key. See: Private key 1 is B2 55 38 35 39 4D 34 8C 85 54 BB EB 14 02 29 91 D4 89 E4 EF 4A F7 20 51 D3 59 5F 8C 23 E1 BC B9
Private key 2 is E2 DC 50 E3 79 E0 EC F8 2D C0 5E 6D A5 08 89 CC 8A 4C CA C2 3F 40 76 76 CD 15 3C 49 C9 AB AB 41
Bitcoin address of summing public keys: 12mMm5FypacB3rcehrBpqaNqwYvF9PSjjE
Bitcoin address of summing private keys: 12mMm5FypacB3rcehrBpqaNqwYvF9PSjjE
Combined private key: 95 31 89 18 B3 2E 21 84 B3 15 1A 58 B9 0A B3 5F A4 27 D2 CA DA EE F6 8C E0 9C 3D 49 1D 57 26 B9
It may be counter-intuitive but it is true and it works. Don't know what else to say. |
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Bwagner: I was just going to post that! That page is part of a very good introduction to the EC math. The start of that intro is here: http://www.certicom.com/index.php/10-introductionnetrin: An analogy with "baby numbers" would go somewhat like this. I have to abstract some cryptography properties though. Person A comes up with a number, say 13, and calls this private key 1. He then calculates the public key, which is (for example) "accb". This public key has the property that it can be easily calculated from the private key, but it also has the property that if you only know "accb", then there is no way to find out the private key was 13, unless you bruteforce all numbers by calculating the public key to all of them. Person B comes up with a number, say 41, and calls this private key 2. He then calculates the public key, which is (for example) "bbbb". Person A gets the public key from Person B, and adds it to his own: "accb" + "bbbb" = "cddd" Person B gets the public key from Person A, and adds it to his own: "bbbb" + "accb" = "cddd" Now they both have the public key "cddd", so they can send money to that public key. To retrieve the money, however, you need to have the private key. The private key to "cddd" is 13 + 41 = 54. But no one knows this! That's roughly how you create a private key that no one knows. I would like to note that this is NOT diffie-hellman secret generation, as far as I know! Neither party knows the private key here, and in fact, any attacker listening to the network could know the private key too. This doesn't matter too much though, since the private key is what you need to get the money. EC diffie-hellman looks similar but is slightly different. In fact it's more like what ByteCoin described early on in the thread. In order not to confuse the thread/topic, I'll just link to the wikipedia page: http://en.wikipedia.org/wiki/Elliptic_curve_Diffie%E2%80%93HellmanThe question is what allows you to assert. ECC(private key 1 + private key 2) = (public key 1 + public key 2) We know these are true: ECC(private key 1) = public key 1 ECC(private key 2) = public key 2 But do we know (as in some whitepaper, mathematical proof, etc) that: ECC(private key 1 + private key 2) = (public key 1 + public key 2) Could you please go throught this tutorial - it does not take that long - and then see if you can see it: http://www.certicom.com/index.php/10-introduction |
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I think we can wait to see exactly what Google checkout customer service says/rules before we determine the final outcome. Give him a chance to work it out with them. Let's see what happens.
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You can send an envelope full of cash to Al's Pawnshop in Canada. No, seriously. That is what I do. He sells them for a 6% discount under the Mt Gox price on the day your money arrives.
It does take a while with the snail mail and all...
If you have a Mt Gox account you can buy Mt Gox redemption codes using PayPal or a credit card at MrCoin.org
Good luck!
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Mt Gox codes are exactly that - a promise of actual BTC. As long as Mt. Gox keeps exactly the number of BTC on account that they have promised in all of their outstanding unclaimed codes all is well with the world - peace, harmony and love. However, if people start using the codes themselves as a longer term store of value or worse yet as a medium of exchange then Mt. Gox may be tempted into issuing more codes than they have BTC and the evil dark lord of fractional reserve banking will rise again  ! As consumers we can prevent this by using the Mt. Gox codes for only a short period of time and claiming them as soon as possible. Also ony accept actual BTC as payment (coins ok as they contain actual BTC) - never accept promises of BTC for payment. There is already a market for the codes. You can buy them with credit card payment at http://www.mrcoins.org Sorry to bring up an earlier post, but I thought I'd address this point for clarity's sake. Mt.Gox Redeemable Codes for either bitcoins or traditional currency automatically "remove" the relevant sum from a user's account on their creation. These funds are then held in limbo until the code is redeemed. As such, it is impossible for a user to create a redeemable code for more funds than they have access to. Since these funds are drawn from a user's account, a redeemable code represents funds which are in existence at the time of its creation, which are held for as long as it takes for the code to be redeemed. Since the actual amount of bitcoins or dollars won't vary in a user's account over time (unlike the value of those funds) then as long as an entity which accepts Mt.Gox Redeemable Codes exists, they will be valid. Of course, this assumes that Mt.Gox does not access, use or alter user's funds in any way (apart from the taking of trade fees), but I hope the community is willing to trust us on that point. If there are any other questions or concerns in relation to Mt.Gox Redeemable Codes, feel free to contact us on the forums, or at support@mtgox.com. Good to know. Be sure to let us know if you ever relax your self imposed reserve requirement! |
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Ordered 5 BTC using PayPal. Worked like a charm. Got my Mt Gox code in seconds. A bit on the expensive side but fun. So far so good. I have been able to order using VISA and PayPal. Richard, Let us know what happens when you get your first charge back request from either a VISA or PayPal sale. I am rooting for you. After buying 1 of the 5 BTC coupons for $16.24 I realized that it was cheaper to by 5 of the 1 BTC coupons for only $16.20 so I did that to cost average my purchase Most of the time when you buy more you get a break. I am sure it is just a rounding error - I am just giving you a hard time  |
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In the two hologram system I outlined in the other thread you would end up with three public key addresses:
1) the public key address of the first hologram P1 (first private key under it - p1)
2) the public key address of the second hologram P2 (second private key under it - p2)
3) the public key address etched or printed on the item itself (bill or bar) P3
It is this third public address, P3, that would have the BTC sent to it, the other two public addresses are not really needed after the item is made and P3 is calculated from them.
To check a bill or bar to make sure it is worth what it says all you would have to do is lookup the third public address (P3) in the block explorer and make sure it contained the correct number of BTC.
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Google's not too helpful either. Going through some material I'm still at step one:
y^2 = x^3 + ax + b
x=4
a=5
b=20
y=11
Are x and y integers, real, or complex?
I didn't understand RSA nor D-H until I could draw them out on paper. This seems like the "Hello World" of cryptography, which is rarely available.
To answer your question if you want to take a stab at it you would need to select a prime number p for your field and then since for Bitcoins a=0 and b=7 your elliptical group generator equation would be: y^2 mod p = ( x^3 + b ) mod p As stated above very tedious by hand. If you pick a small prime like say 13 then there will be only 13 points that will satisfy this equation and those 13 points will form your elliptical group. Then you would need to learn how to add two of the points together - not trivial but you can look it up or I can give you the equations EDIT: Just read the previous post which includes what you need to add points so I don't have to look it up! |
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