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Author Topic: Have you seen this? Litecoin much more secure than bitcoin (as a fxn of time)  (Read 510 times)
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April 22, 2013, 12:50:36 AM

A repost for your convenience:

This came out of some research I put into finding out the probability of a 51% attack for bitcoin. You'd think that mining 6 blocks in a row would be hard to do, even with 50% hashing power, because most people would probably think about a coin flip and how likely it is to flip 6 heads in a row. Intuitively it seems like a hard thing to do but in reality, if you do it enough times, it becomes not only possible, but downright likely, even with a mere 100 coin flips (warning:pdf).
With bitcoin mining 144 blocks per day a 51% attack with 50% hashing power is just as likely. Even with 35% hashing power it's relatively trivial to pull off. The reason most people probably haven't thought about this before is because the math itself isn't very straitforward. According to, it is a tough question to answer with a simple formula. Thankfully there are computer programs which can do this. This site has a javascript "streak" calculator that will calculate the odds of a doing a 51% attack. Just put in 1008 trials for a 1 week period (6*24*7), your streak length of 6 blocks, and a probability of .35 for 35% hashing power. The result is about a 70% probability over a 1 week period and a 99.2% chance over a 1 month period.
Sense all the legwork had been done solving this problem for bitcoin I thought I'd run the math again for litecoin and what I found is actually quite surprising. Litecoin isn't just more secure than bitcoin, it is orders of magnitude more secure than bitcoin.
Gambler's Ruin / why litecoin is more secure than bitcoin:
I figure the reason is in both cases you're trying to "beat the odds" and mine every single block for a 1 hour period but with more "roles of the dice" occuring during that same period of time it's a lot harder to keep up your winning streak with litecoin than it is for bitcoin.
While a bitcoin pool with 35% hashing power can reasonably expect to be able to pull off a 51% attack within one week, that same hashing power for litecoin makes it almost impossible, not just for a 1 week period, but for an entire year, even for 100 years!
The numbers here are 4,032 trials per week and 24 blocks in a row. The result is 0.0000029760539%. The same problem over a month and a year is about the same and over 100 years the probability is a mere 0.0155609472527%. At 50% hashing power and 100 years an attacker has a 46.46% chance (6.06% for a 10 year period) but bitcoin hits both those thresholds in under 1 day. At 100 years bitcoin is vulnerable to a miner holding just 8% hashing power, while litecoin remains secure all the way up to 50%. No matter how you run the numbers litecoin remains significantly more secure -- entire worlds more secure -- than bitcoin.
How many litecoin blocks give you similar security to bitcoin?
With the numbers so dramatically in litecoin's favor one would assume you'd need overall less time to verify a transaction with litecoin than you would with bitcoin. Generally we have assumed it takes 4 litecoin blocks to equal the security of 1 bitcoin block but this has always been a guess. Even the people who run the litecoin-project on github know this isn't true (see bullet #3 on Faster transaction time). The problem again is the math not being a simple equation that you can easily solve for but using that same calculator at the 50% threshold I've found that 8 litecoin blocks give you about the same security as 6 bitcoin blocks.
The nature of this problem is that it's not a linear relationship -- at 30%, 8 litecoin blocks are about twice as secure as 6 bitcoin blocks, but droping to 7 litecoin blocks and then to 6 very quickly tips things in bitcoin's favor. The only scenareo where litecoin is less secure than bitcoin is when you compare the two networks block to block. As a function of time litecoin is significantly more secure, so much so litecoin offers similar security at 20 minutes as bitcoin does at 60 minutes.
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