My statement is only a trick, 'fake chain' 'hypothesis' of a computational complexity of O(2^(log n)/n) for 'forging' a chain of length n, where n is the number of blocks in the chain. (A difficult task because the hash of each block in the chain is based on the previous block's hash, so changing any part of the chain would require recalculating the hashes for all subsequent blocks).
By the way, forging a chain refers to the act of creating a 'fraudulent chain' that appears to be legitimate.
I think O(2^(log n) / n) can be broken down as follows if you’re familiar with mathematics:
log n: Logarithm of n, which is the exponent to which 2 must be raised to obtain n. 2^(log n): Equivalent to n, since 2^(log n) = n. & 2^(log n) / n: will represent the ratio between the amount of work required & the size of the input.
"2^(log n)" is essentially another way of writing "n", because 2 raised to the power of log n gives you n. So you can think of this part as n/n, which simplifies to 1.
Consequently, the computational complexity can be simplified to O(1/n). This means that as the length of the chain (n) increases, the computational requirements for forging a chain increase, but not proportionally.
Specifically, the computational requirements decrease as the length of the chain increases.
Simply, it becomes exponentially more difficult to forge a longer chain, which is a desirable property for a 'secure cryptographic system' like #Bitcoin.
