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Which is the best overall hashing algorithm in terms of complexity and security? md5 or sha1?
From what I know md5 is faster than sha1 but SHA1 is more complex than md5.
Am I missing anything?
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Algorithmic complexity is a measure of how long an algorithm would take to complete given an input of size n. If an algorithm has to scale, it should compute the result within a finite and practical time bound even for large values of n. For this reason, complexity is calculated asymptotically as n approaches infinity.
The complexity of an algorithm can be divided into two types. The time complexity and the space complexity.
When we analyse an algorithm, we use a notation to represent its time complexity and that notation is Big O notation. For Example: time complexity for Linear search can be represented as O(n) and O(log n) for Binary search (where, n and log(n) are the number of operations).
If your algorithm runs in a time proportional to the logarithm of the input data size, that is log ( n ) \log(n) log(n), then you have O ( log ( n ) ) \mathcal{O}(\log(n)) O(log(n)) complexity. This type of complexity is usually present in algorithms that somehow divide the input size.
First of all, MD5 is broken - you can generate a collision, so MD5 should not be used for any security applications. SHA1 is not known to be broken and is believed to be secure. Other than that - yes, MD5 is faster but has 128-bit output, while SHA1 has 160-bit output.
Update: SHA1 has been broken: a team of researchers at Google and CWI have published a collision - https://shattered.io/static/shattered.pdf
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