Quote from: GreenLighter on December 20, 2016, 12:45:59 AM

Quote from: JFC on December 19, 2016, 01:18:44 PM

Quote from: GreenLighter on December 19, 2016, 12:30:37 PM

There would be duplicates

Could you please elaborate?

In two ways. First, there are bound to be more than one Bitcoin address bound to certain keys. Easy to fix this one by increasing the amount of number slots. Second, by using a smaller pool of characters, you are more likely to generate the same address multiple times. This is why Bitcoin uses base58. If characters that look similar to you are not a problem, you could expand it to base64, increasing the address possibilities significantly. Taking it a step further, which would add 0, O, I, l you could add other characters like !@#$%)^()& to add even more

Hi, thanks for your extended comments.

I think you are missing a key element of this system to express an address.

As a precondition, the intended address must exist already in the blockchain. You can't use this scheme to represent a new address that you have generated but no one has seen yet.

So, you are counting the addressing capacity of this scheme the wrong way.
This address scheme is not a way of shortening any arbitrary bitcoin address by expressing it with only decimal digits.
Any such schemes are obviously destined to fail since you can't express the 2¹⁶⁰ addresses with a few decimal characters. (You'd need up to 49 decimal digits, to be more precise; that is 0 .. 1461501637330902918203684832716283019655932542975 ).

But, given the precondition stated above, we don't need to be able to represent every possible address. We only have to be able to express an address that is already recorded in the bitcoin blockchain.

So, this address scheme is simply a secure and human friendly way to represent a pointer to an existing address.
As a result, we only need enough digits to express the pointer, like this (I am showing here the more complex case, where you can have different outputs in a transaction):

Quote

Pointer to the block . Pointer to the transaction . Pointer to the output . Checksum

How many decimal digits do we need to express any bitcoin address already recorded in the blockchain as a transaction output then?

Let's count them :

Pointer to the block -> 6 digits.

We are around block 444.000 nowadays, after 9 years of constantly producing blocks. At this speed (1 block every 10 minutes) we won't need more than 6 digits for ten more years.

Pointer to the transaction -> 4 digits (máx) Depends on the block size. Nowaways 4 digits. I don't think we'll need more than 5 digits for a long time.

Pointer to the output (within the transaction) -> 4 digit (máx) .

According to Gavin Andresen transactions larger than 100K won't be relayed. That means fewer than 2000 outputs per transaction.

Checksum -> 7 digits (max) (I am counting on using the last 5 hex digits of a SHA256 hash to have a risk of an undetected error smaller than one in a million).

So, you need 6 + 4 + 4 + 7 = 21 decimal digits in a worst case scenario nowadays (not counting decimal separators and the BTC prefix). Most of the time, you'll need around 6 + 3 + 2 + 5 = 16 or 17 decimal digits.