2200+ entries in 0.333s
BingoBoingo:
^ Summary of what thing is thus far, comment and especially criticism welcome.
mircea_popescu: it may appear beneficial to instead produce larger sets, such as of 4096 bits. the UPPER BOUND of the gain from this process is known ; the lower bound of losses from it is not known, because yes if you allow 4096 bit p, q and test, an acceptable N can be composed of the product between 17 and 2
^4092 - 177 or whatever it was.
a111: Logged on 2017-11-14 11:33 apeloyee: diana_coman: if keeping the minimum of 2
^2047 for primes, you can, for example, generate primes between 2
^2047 and 2
^2049, and start over if the modulus is unacceptable. not sure what minimum for p and q makes sense.
mircea_popescu: trinque
^ that sound like sense ? "you get this rack for a year, to be paid $x every mon" ?
mircea_popescu:
^ 20 acre compound in bucarest. started production 62.
mircea_popescu: asciilifeform how is a 1GB ram chip store the 2
^30 bits ?
mircea_popescu: nevertheless, the correct solution to this "quickly, prime this many bits long" is a n, k tuple which contains n as the bitsize and k as the "oddness". if you want the n - 396 k = 5 prime you get 2
^396- 1229
mircea_popescu: if you want an n bit prime calculate 2
^n and substract the correct small integer.
mircea_popescu: asciilifeform there's much faster ways, such as the 2
^x - y method.
a111: Logged on 2017-11-14 11:33 apeloyee: diana_coman: if keeping the minimum of 2
^2047 for primes, you can, for example, generate primes between 2
^2047 and 2
^2049, and start over if the modulus is unacceptable. not sure what minimum for p and q makes sense.
mircea_popescu: of course, the odds of getting a FF FF q and a FF FF p are 1/2
^32
a111: Logged on 2017-11-14 11:05 apeloyee: if M is say, 1.999999 * 2
^2047, then ~20 first bits of p and q are known
a111: Logged on 2017-11-14 11:02 apeloyee: if the modulus is M, then p,q>M/2
^2048 (because p,q<2
^2048)
diana_coman: asciilifeform, I meant in the final pair; i.e. you get p=3 and q=2
^4095+1 sort of thing; ofc throw both in a pair if product not right size; but if not enforcing any size condition at all on p and q then you can end up with any small prime too
apeloyee: diana_coman: if keeping the minimum of 2
^2047 for primes, you can, for example, generate primes between 2
^2047 and 2
^2049, and start over if the modulus is unacceptable. not sure what minimum for p and q makes sense.
☟︎☟︎ apeloyee: grrr. "M is say, 1.999999 * 2
^2047" << 2
^4065, of course
apeloyee: if M is say, 1.999999 * 2
^2047, then ~20 first bits of p and q are known
☟︎ apeloyee: if the modulus is M, then p,q>M/2
^2048 (because p,q<2
^2048)
☟︎ apeloyee: fwiw I just realized that this
^ leaks a little via the modulus
a111: Logged on 2017-11-13 21:10 asciilifeform:
^ pheeature idea : why not have ticker autofire when the number moves >10% from last tick
mircea_popescu: asciilifeform no, because see, if you don't use nextprime you lack the "nop bridge" so to speak. rolling number 6 does not take you to 7. to get 7 you need a natural 7, and this is equiprobable to rolling a natural 2
^74207281-1 on the space of (0,2
^74207281-1).
a111: Logged on 2017-11-13 12:44 mircea_popescu: this is not "true for very many keys like a billion trillion keys". this is true all the way up, by the time one's made 10
^609 keys we're starting to get into five-nines assurance of unicity.
mircea_popescu: this is not "true for very many keys like a billion trillion keys". this is true all the way up, by the time one's made 10
^609 keys we're starting to get into five-nines assurance of unicity.
☟︎ mircea_popescu: anyway, back to rsa discussion : there's about 6.5e612 primes in the interval 2
^2045-1, 0 (by teh prime number theorem). every key needs a pair of these, and no number can EVER be repeated (if it is -- phuctor breaks both keys).
mircea_popescu: the reason you stick the 2nd 1 in front is, not evidently, also to not end up with sub-4096 Ns : if you had the exceptional case of your primes being each 2
^2047 + 1 your N would then be 2
^4094+2
^2048+1, which is shorter than 4096 bits.
spyked:
^ and if it does, should be easy to plug it in.
mircea_popescu:
^ that is my key. and because ~everyone knows it, that same ~everyone can tell whether it's me talking or some impostor.
shinohai: Espero k tengas un dia muy bestial! =
^.
^=
a111: Logged on 2017-11-02 19:33 asciilifeform:
^ per asciilifeform's current understanding, thing is untriangulable unless enemy knows the freq keying pattern, or is standing in the near field of your transmitter.
shinohai: oh hai mod6 .... happy Friday! =
^.
^=
a111: Logged on 2017-11-02 19:33 asciilifeform:
^ per asciilifeform's current understanding, thing is untriangulable unless enemy knows the freq keying pattern, or is standing in the near field of your transmitter.
diana_coman: mircea_popescu, huh, not that clear in my text, is it; will update; specifically: with 12 iterations probability that M-R falsely returns prime on a non-prime is less than (1/4)
^12
mircea_popescu: diana_coman is m-r upper-bounded by 1/4
^ 12 ? or lower ?
a111: Logged on 2017-11-01 20:31 asciilifeform:
^ approx. a ro-flavoured 'широка страна моя родная'.
a111: Logged on 2017-10-31 18:58 asciilifeform:
^ complete with megatonne of perverse and pseudolegalistic jesuitry, almost custom trololol for mircea_popescu .