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RSA-768 took 2000 years of 2.2Ghz single core Opteron from year 2009 [1].
DJB et al wrote in 2013 [2] that RSA-1024 would take $2^{70}$ differences with $2^{24}$ per machine per second in 2009, so 2 million years. Hardware improved since then, and GNFS can use GPUs, so maybe better, but about a million years I guess.
Absolutely the computation can be ...
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Whenever you see the letters ECB, you should run away screaming. This is a telltale sign that something has gone terribly, horribly wrong. The code fragment you quoted implements what we sometimes call ‘textbook RSA’, which is a polite way to discreetly announce to the cocktail partygoers that you are desperately in need of a professional cryptographer.
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is it because we already know the output or why ?
It's one of the strategies we use to turn a distinguisher (which a differential or linear characteristic) into a key recovery attack.
Here's how it goes; suppose we have a distinguisher that works over R-1 rounds, that is, given a number of plaintext/ciphertext pairs, it can tell us (with advantage over ...
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The measure of resource typically used to evaluate memory-hard functions is not the amount of work (i.e., $T$-complexity) but rather the space-time complexity (i.e., $ST$-complexity) of the computation. As the name suggests, it is the product of the maximum amount of space used and the time taken for the computation. (Strictly speaking, we have to also take ...
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There is a much better explanation available. See Graham Ellsbury's page here for full details, and a summary below:
Intuitively, what one does first is to drag the crib (known plaintext) accross the ciphertext and rule out relative positions which map a plaintext letter to itself in the ciphertext (since it is known that the Enigma mapping has no fixed ...
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