Camo Banano Amounts

Camo Banano Amounts.md

Storing and transferring hidden amounts on the blockchain using ECDH.

This gist will describe how to use ECDH to transfer hidden amounts in a blockchain.

first start out with two private keys:

  "privateKey0": "0000000000000000000000000000000000000000000000000000000000000000"
  ,
  "privateKeyF": "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"

next compute three shared secrets:

  // shared secret between privateKey0 and itself.
  "sharedSecret00":"12237211748635139837530061043450201432206441889892237319568051592877041511923"
  ,
  // shared secret between privateKeyF and itself.
  "sharedSecretFF":"82875262223760956416988601125860915766933841244206307108290578087849094219521"
  ,
  // shared secret between privateKey0 and privateKeyF.
  "sharedSecret0F":"57739338942242553750896228776014673335567092091103501790731983178173264663502"

The account with privateKey0 knows sharedSecret00 and sharedSecret0F.

The account with privateKeyF knows sharedSecretFF and sharedSecret0F.

privateKey0's current balance in the blockchain is oldBalance0 = (oldAmount0)x(sharedSecret00).

privateKeyF's current balance in the blockchain is oldBalanceF = (oldAmountF)x(sharedSecretFF).

To transfer an amount0F from 0 to F, you must compute three things:
amount0F = (amount)x(sharedSecret0F).
newBalance0 = (oldBalance0) - (amount0F).
newBalanceF = (oldeBalanceF) + (amount0F).
privateKey0's new balance in the blockchain is (newBalance0).
privateKeyF's new balance in the blockchain is (newBalanceF).
You must then prove two things:

1. to create the send block, the chain needs to confirm:
   newBalance0 = oldBalance0 - amount0F;
   I.E. (newBalance0) + (amount0F) = (oldBalance0)
   I.E. ((newAmount0)x(sharedSecret00)) + ((amount)x(sharedSecret0F)) = ((oldAmount0)x(sharedSecret00))

2. to create the receive block it needs to confirm:
   newBalanceF = oldBalanceF + amount0F;
   I.E. ((newAmountF)x(sharedSecretFF)) + ((amount)x(sharedSecret0F)) = ((oldAmountF)x(sharedSecretFF))