Wikipedia:Reference desk/Archives/Mathematics/2016 August 6

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August 6

Digits of pi and cryptography

I have heard anecdotally that there are instances in cryptography (related to elliptic curves?) where you need a large number of digits of pi (much more than the 39 digits that is said to be enough to measure the radius of the universe). Is this true, and if so why? 24.255.17.182 (talk) 01:42, 6 August 2016 (UTC)

Perhaps you are referring to the cypher described here [1], though it's nothing to do with elliptic curves. Basically you can take any pseudorandom sequence and XOR it with your plaintext to get the ciphertext. In this case you're using the digits of pi as the pseudorandom sequence. This is a variation of the old book ciphers where each word to coded as the location (page, line, position in line) of the word in a known reference book. I gather that the problem with this type of code is that once you know how it works (the book used or the random number algorithm) anyone can decode the message; see the responses in the link. One-time pad has some additional information. One of the requirements is that you need truly random (e.g. flip a coin a million times), not just pseudorandom (e.g. binary digits of pi) bits for it to work. --RDBury (talk) 02:59, 6 August 2016 (UTC)

You may be referring to nothing up my sleeve numbers. When a cryptographic algorithm uses some predefined constants, as many do, there's always a risk that the designer chose those numbers to have some special non-obvious characteristics that provide a cryptographic backdoor. Using a well-known constant like pi makes it highly unlikely that there's anything special about the chosen constants. CodeTalker (talk) 18:09, 6 August 2016 (UTC)

The Brainpool elliptic curves use 1120 bits (about 337 decimal digits) of pi as a nothing-up-my-sleeve number (see CodeTalker's answer). Blowfish uses 30,000+ bits of pi as a NUMS number, but it isn't ECC. -- BenRG (talk) 19:30, 6 August 2016 (UTC)

Paper for learning math: squared, lined, graph, dotted or plain?

I suppose I have not forgotten any kind of paper. If I have, please feel free to suggest it.

What kind of paper is more appropriate for learning math? Is plain paper better if you want to scan your notes after a while and throw the paper away? Would plain paper force you to pay more attention? --Hofhof (talk) 18:23, 6 August 2016 (UTC)

It depends what sort of maths you're doing. My school books used squared paper, because it ensures your columns line up when you do arithmetic. Graph paper is of course good for graphs, lined paper for writing out notes in prose and for writing out formulas, plain paper for geometry and so on. Smurrayinchester 21:28, 6 August 2016 (UTC)

I vote for plain paper. Put it in your printer and print out all the math you've done on the computer, if you really need a hardcopy. If not, leave it online. An exception is integration, etc. where you have weird multi-line symbols that computers don't do very well. StuRat (talk) 00:57, 7 August 2016 (UTC)