# Minority Attack on Bitcoins

I read the first paper which described the bitcoins. Most of it is clear except for one thing. I tried to find solutions online but couldn't find it.

I am completely aware of the implications of a regular majority attack and how it is carried out, the other resources required for it and the consequences. The question below is completely different from it.

The paper by Satoshi Nakamoto claims that bitcoin is secure when >50% of precessing power is controlled by good people(non-attacker). This means that the chain mined by good people will grow the fastest and the probability that the attacker will be able to catch it will be exponentially low. But consider a case when 51% of processing power is with good people and 49% of cpus have joined hands to attack the network. Now each good node might get transactions in different order. Further the first transaction in each block is special which pays to the creater of the block. So basically each good node is trying to hash a different block while all the attackers are trying to hash a single block. Isn't it that the attackers can hash the block much faster than good people. Thus their chain has one extra block at this step than good people.

I have already asked few people but couldn't get any satisfactory answer to it. Neither could I find anything which addresses the difference of block for good people online.

• Hi Akash Garg, you should try looking into the tag majority-attack, it collects all questions related to your topic. I think this question may be a duplicate of What can an attacker with 51% of hash power do?.
– Murch
Mar 5 '17 at 20:36
• Hi Murch, thanks for the tag. I appreciate your help. And about the duplication. I clearly understand what will happen when attacker holds 51% or more power. It is the most basic case. I read the answer as well and I am well aware of the derivation. My question is about security when attacker has 49% or less power. Can we guarantee security if attacker has <= 49% power. The case I have described above, the attacker holds exactly 49% of cpus and good people 51% but still security is not guaranteed. Mar 6 '17 at 4:42
• You're right, due to the efficiency of scale, the attacker doesn't actually require a majority of the hashrate. At least for selfish mining there have been dozens of papers showing that it might even be sufficient to have 25% to gain more than your fair share in mining. I'm not sure if there has been a paper for majority attacks along those lines.— Perhaps you could edit your question a bit to make this point stand out more and be reflected in the title. Please also mention that you're aware of the implications of a regular majority attack.
– Murch
Mar 6 '17 at 8:03
• Thanks for the suggestions. Also this thing can be linked to mining groups. A mining group can actually use this way to gain more than fair share. A group where all people are trying to mine the same block controlling x% of processing power is more likely to hash faster than other x% of processing power which is divided into individual units each mining different block. Mar 6 '17 at 14:20
• Yes, in this context also see selfish-mining
– Murch
Mar 6 '17 at 14:25