is this position still open ?

from what I have read,

a private key is a 256 bit binary number.

private key ----------elliptic curve multiplication-----> public key

public key -----------sha256 + ripemd160 -----------> public key hash

public key hash -------base58 check encoding------> bitcoin address

now according to the above,

2²⁵⁶ private keys are possible
since elliptic curve multiplication produces a unique public key from each private key, an equal number of corresponding public keys are also possible. But, since the public key goes through RIPEMD160, the public key hash has only 20 bytes or 160 bits. Hence only 2¹⁶⁰ bitcoin addresses are possible. Does this mean that each bitcoin address may be associated with more than one private key? Since, if each of 2²⁵⁶ public keys produce only 2¹⁶⁰ hashes this means more than one public key produces the same public key hash.

I would appreciate if an expert could clarify this matter ?

true, this is correct as far as the possible addresses are concerned, but someone who is trying to find the correct private key using brute force will have to try all 2²⁵⁶ private keys, since there is no way to determine which of these will not be linked to a valid address.

however i admit that my statement above is not entirely correct

IMHO there are two matters to be considered in answering this question

(1) It is the total miner fees for all transactions in the block that is expected to be more than the block reward. Currently, there are between 1000 to 3000 transactions per block. This is expected to increase as bit-coin becomes more popular.

(2) This situation is expected to occur in the future and not immediately. Perhaps, when mining reward is less than 1 BTC (just guessing, it may be before, it may be after, but most probably not in the near future)

A private key is a 256 bit binary number. When written in hexadecimal this comes to a 64-digit hexadecimal number, which in decimal is approximately 1.158 x 10^77. Each private key will produce a unique public key and corresponding bitcoin address. So there are 2^256 possible combinations of private key, public keys and bitcoin addresses.

To get an idea of the numbers we are dealing with consider the following.

The world's fastest super computer is currently capable of performaing 33.6 quadrillion (33.6 x 10^15) calculations per second. Even if we assume that this makes it possible to check one private key per calculation (the actual number will be less since checking whether a particular private key agrees with a given bitcoin address will need much more than one calcultion), it would need 3.45 x 10^60 seconds or 1.1 x 10^53 years to try all possible private keys. So to try and steal bitcoins that are at a particular address by trying all possible addresses, though theoritically possible is computationally infeasible.

eCoin (just like email, ebook, ecommerce, ebay, e-this, e-that etc.)

isn't this related to the manner in which the difficulty target is recalculated, as defined by the developers ? am I correct in understanding that if the 10 minutes average is to be brought down, some change will need to be done to the code that recalculates the difficulty every 2160 blocks ?

you can join http://cryptotalk.net and start posting. It is a forum where you get paid 0.0001 BTC per post for posting. You can claim a payment after making 25 posts. Many bitcointalk members have signed up and have already received payments. Please educate yourself on the rules before posting, and don't spam the forum with copy/paste posts from various websites. It won't make you rich in a short time. But you can get a few coins to get started and move on to better ways of earning later.

The Bitcoin system has been designed so that the reward for mining a block is halved after every 210000 blocks. When block 0 (also known as the genesis block) was mined in early 2009 it was 50 BTC (five billion satoshi) https://blockchain.info/block-index/14849/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f

The first halving took place on reaching block 210000 towards the end of 2012, after which the reward for mining a block became 25BTC (2.5 billion satoshi) https://blockchain.info/block-index/270670/000000000000048b95347e83192f69cf0366076336c639f9b7228e9ba171342e It remains at this value today and will continue untill reaching block 419999. From block 420000 the reward will be 12.5 BTC.

It is generally mentioned that the total bitcoins that will ever be mined is approximately 21 million BTC. The math involved here uses geometric progressions (GP) . This is an ordered sequence of numbers where each number (or term) is obtained by multiplying the previous number by a fixed amount. e.g. consider the sequence 1,2,4,8,... here the fixed amount is 2. This is known as the common ratio of the geometric progression and is referred to by the letter 'r'. The letter 'a' is used to refer to the first term of a GP. So for the above GP a = 1 and r = 2.

If the common ratio (r) is a fractional value less than 1, this results in a GP where the terms decrease. e.g. 100000,50000,25000,12500,6250,... is a GP where a = 100000 and r = 1/2. GPs that have such common ratios are said to be convergent. It is a property of all convergent GPs, that the total obtained by adding any number of terms in such a GP (no matter how many terms) will always be less than a fixed value reffered to as the 'sum to infinity' of the GP. We shall refer to this as 'S'. It is obtained according to the simple formula given below

S = a/(1-r)

In other words, to obtain the 'sum to infinity' of a given convergent GP, subtract the common ratio from one, and then divide the first term by the answer obtained. Accordingly, for the GP 100000,50000,25000,12500,6250,... where a = 100000 and r = 1/2, S = 100000/(1-1/2) which gives 200000. What this means in practice is, that no matter how far we continue the above GP, the total obtained by adding together all the terms will always remain below 200000.

Now, let us see how this applies to Bitcoin. Here we will form a GP where the terms will be the total mining reward for a group of 210000 blocks.

for block 000000 to block 209999 total reward = 50 x 210000 = 10500000 BTC
for block 210000 to block 419999 total reward = 25 x 210000 = 5250000 BTC
for block 420000 to block 629999 total reward = 12.5 x 210000 = 2625000 BTC
for block 630000 to block 839999 total reward = 6.25 x 210000 = 1312500 BTC

and so on

It can be seen that we get a GP where a = 10500000 and r = 0.5 (or 1/2)
from this we can see that S = 10500000/(1-0.5) = 21000000

this means that the total reward obtained by mining all blocks that exist at any point in time (whether in the past or the future) will be less than 21000000 BTC. Since it is the bitcoins produced through mining that enter and circulate in the bitcoin economy, this means the total BTC in circulation will always be less than 21 million BTC. It should be noted that this also means that exactly 21 million BTC will never come into existence.

The table given below shows the mining reward in satoshis per block as the block chain grows
( 1 BTC = 100000000 satoshi )


Since 1 satoshi is the smallest unit of transaction in the Bitcoin system, when halving results in fractions of a satoshi, the fractional part is discarded. This will first happen on reaching block 2100000 and many times thereafter until ultimately the block reward comes down to 1 satoshi on reaching block 6720000. This means that from block 6930000 there will be no mining reward, and hence no new bitcoins produced through mining. At such a time miners will only get the tranaction fees, but it is expected that by such time the value of 1 BTC will be high enough for transaction fees alone to be sufficient compensation for miners.
If we use the above figures and calculate the total quantity of BTC produced, the figure obtained is 20999999.97480000 BTC, which is 2520000 satoshi less than 21 million BTC, and confirms the fact that the total BTC mined will be less than 21 million BTC as mentioned above.

The Bitcoin system has been designed so that new blocks are produced through mining at an approximate rate of 1 block per 10 minutes, which comes to around 144 blocks per day. So the time taken to reach block 6930000 should be 6930000/144 = 48125 days, which is a little less than 132 years. We know that the genesis block was mined, most probably by Satoshi Nakamoto himself, on 03-01-2009 as indicated on the blockchain at https://blockchain.info/block-index/14849/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f. This means that by the end of 2140, block 6930000 would be reached. This is why it is said that the last satoshi would be mined in 2140, and that no new bitcoins would ever be produced thereafter.

hello sir,

my membership has been removed and all my posts are gone. I don't think I have broken any rules. I have registered again with the same username and email. Could you please explain what's going on. If you don't like some of my posts you could just remove them, without removing everything. I hope this is just a mistake.

Here are some suggestions to the admin of cryptotalk.net to maintain the quality of the content posted on the forum

(1) Make it compulsory for new members to post a request for membership in the rules section, where they should introduce themselves and explain in at least 100 words what type of content they wish to contribute to the forum etc. Membership should only be granted after this is approved by the admin or mods who are appointed by the admin for this purpose.

(2) After the above approval is granted moderate the first 10 posts of every new member, especially new topics started by them

(3) When the first request for payment is made, if 20 or more posts are "copy and paste" posts, along with rejecting the request, ban the user and remove all topics started by him/her. Generally, legitimate users will not bother posting under these topics so it will not affect their post count significantly

(4) If 20 or more posts are "copy and paste" posts in subsequent requests for payment, delete the offending posts and also topics which have been started with an offending post

(5) When there is a legitimate reason to copy and paste content from a website, introduce a standard format for it.

(6) Define a "copy and paste" post precisely - e.g. any post with more than 50 words where 80% or more of the content appears exactly as posted in another website or forum.

the forum is getting filled with copy and paste posts, by users who are trying to earn something easily. The admins should do something to arrest this trend and nip it in the bud. It creates a bad impression for a casual visitor.

Hello, this is my first post. I am posting here because this is exactly the topic I need help in. If necesary I will start a new thread.

I have successfully managed to prepare and sign raw transactions using Coinb.in and broadcast them. I would like instructions on using bitcoin-tx. So far I have managed to get the raw hex output for an unsigned transaction from bitcoin-tx and get it signed using Coinb.in, but this is ugly and I would like to do the signing part also using bitcoin-tx.

I used the wallet restore function and made a new wallet using a hexstring taken from the output of

echo -n "My own string"|sha256sum

in a linux conole. If a truly unique string (perhaps involving personal informtion) is used for "My own string" which can be easily remembered, (e.g. "cyberguy was born on the 29th of February 1976 in the middle of the atlantic") what are the security implications of this. Could this be considered an alternative for a "brain wallet"