Quote from: Jace on December 12, 2013, 01:16:24 PM

Quote from: no_alone on December 04, 2013, 11:01:25 PM

What is the best way to be absolutely sure my address is random|?
Has anyone ever thought about this issue?

Same here, I am extremely paranoia about this.

Almost 100% secure: just create them as brainwallets from very long random input strings. Obviously you don't need to remember these, they're meant for cold storage so they're not actual 'brainwallets'. They're just created in the same way as brainwallets, i.e. the private keys are hashes from strings. This rules out any dependency from random generators with possible weaknesses.

When I say 'very long random input strings', I mean garbage like this: (just typing a bunch of gibberish characters)

Code:

fY72^og(fU FO!MNxTL/rwA q2kd#plv0ni40X.e4 7n7*4nv5^3u 2_14h D!IQZD6k3L7n

For this particular example, the private key would be Sha256("fY72^og(fU FO!MNxTL/rwA q2kd#plv0ni40X.e4 7n7*4nv5^3u 2_14h D!IQZD6k3L7n") = eab9498f0c866509a2ff09fa40b556776f54b78f941f36cc69bdbf7832f45473, or expressed in more common Bitcoin format: 5KbfHWM9R2AKhoAtkcTDv6agnzJoPCHZkrEnSy8t8bnVTUHJnND and its corresponding address is 1FtUbMx47zhF3AUWTWCULQzDyRJgVDV23G.

Now, to compensate that last bit of paranoia (and just in case some day an entropy weakness is discovered in Sha256 or something), I took this one step further, and created the private keys for my 'big savings' addresses as three xorred hashes:
(1) Some generated (pseudo?)random private key (using bitcoind or bitaddress.org or whatever)
(2) The Sha256 hash of some long random garbage string
(3) The Sha3-256 hash of some different long random garbage string

So for example:
(1) = 5K2F4Ng3ZYx9s98yEj1ukm1boGEHrAt5rMxXy2cnRdMuQtgTVE7 = 9ed845749f418efc834f1b9b5fd0c1765e7ace2177153a59dc818d6ac5df6232
(2) = Sha256("wP7fB2-fo#90wZ7d 4p6.Z1Ug5r H!0tI6*gp7!zcn)V bw4!Qib") = 7220f93d3a8059d19a3a1be4a2e1c3294185ffcae61aece0d02d73d43f9840d2
(3) = Sha3-256("v5!0ZF%kv 2p0isI*yWJ dky3R7Q#en!4X6;UGS-v35r U#aw/5{61ca") = b6783aadb56f8228feb9673eaf15184417ecc3a1e854ed75bf26de1b126c1c26

Xorring these three gives 5a8086e410ae5505e7cc674152241a1b0813f24a795b3bccb38a20a5e82b3ec6 which results in 5JW9LPbpY1b8aLd8MHkZBCtSCbmA29oaHA1jmpf5dWAEntfYo58 / 13wCBWBnQ86kKHBztMm3j44wb53RYP8LuQ.

I'm quite convinced it doesn't get any more secure than this, in terms of private key 'randomness'.

How long would you say the random garbage string needs to be? 100 char? 200?

This intuitively seems more secure than 100 rolls of dice since that would make a string of numbers, whereas these garbage strings are full of numbers, letters, characters, and spaces.

Do you just make a new text document, mash your keyboard, then copy/paste the string into a brain wallet in bitaddress? Assuming this is all done on a computer that will never and has never seen the internet and on wired peripherals, of course.