Are there encryption algorithms based on transcendental numbers? Is it just theoretical or are they implemented in practice? If so, how useful is brute force attacks against them? (My understanding of brute force is that -in simple words- the computer keeps trying each key until it gets it right. But transcendental numbers are not definite, right?)

I will be so greatful for the answer. I am a mere beginner, so please go easy (don't complicate things by using highly technical words and math equations). Thank you

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    $\begingroup$ Cryptography tends to represent messages and keys using finitely many bits, and that goes against using arbitrary transcendental numbers. $\endgroup$ – fgrieu Feb 20 '18 at 8:52

Not that I'm aware of. Certainly nothing widely considered to be secure.

Computers use bits, which can represent integers exactly. Pretty much all cryptography treats its inputs as a bunch of integers.

The smallest possible 64-bit floating point number (the usual format to represent non-whole numbers) has about 16 digits of precision. So pi (for example) would be represented as 3.14159265358979 exactly. There are no transcendental numbers for computers. Changing to another format simply extends the issue, since the amount of memory is still finite. No infinitely long value can ever be represented exactly.


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