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e S- b4t or^t1 fu e t - t "RSA-640", a 640 bit - PDF document

Sep 13, 2022 •343 likes •435 views

kg* M'rnclf6 -a c ct- /cl.eV t Cr utl17-? M ?tl * 5a l,ila cv naw *V olqtl'-t eqolrr44lV hov nrb* v? gt-a,sb t*1h1"'7 t fn(7rl* 'e e S- b4t or^t1 fu e t - t "RSA-640", a 640 bit (193-digits) number was factored in

  1. kg* M'rnclf6 -a c ct- /cl.eV t Cr utl17-? M ?tl * 5a l,ila cv naw *V olqtl'-t eqolrr44lV hov nrb* v? gt-a,sb t*1h1"'7 t fn(7rl* 'e e S- b4t or^t1 fu e t - t

  2. "RSA-640", a 640 bit (193-digits) number was factored in 2005 using 30 CPU-years on a cluster of 2.2 GHz Opterons (5 months elapsed). The 9 n log 2 H n L graph below extrapolates this to other lengths, assuming complexity scales as: 3 64 ‰ In[150]:= f @ n _ D : = Exp @H 64 ê 9 * n * Log @ n D ^2 L ^ H 1 ê 3 LD Show @ LogPlot @ f @ n D ê f @ 640 D * 30, 8 n, 350, 640 * 2 < , AxesLabel Ø 8 "Length H bits L ", "Effort H CPU - years L " <D , ListLogPlot @88 640, 30 << , PlotMarkers Ø 8 Automatic, Medium <DD Effort H CPU - years L 10 8 10 5 Out[151]= 100 Ê 0.1 Length H bits L 400 600 800 1000 1200 If you're worried about someone spending 30 CPU-years to crack your email chatter, what could you do? Double your key length. That will slow en-/decryption by < 8 x (they're sub-cubic algorithms), but slow factoring by 10^8 x.

  3. 'Eqf-640", gO (1g3-digits) a 640.bit number was factored in 2OO5 using CPU-years on a cluster ot 2.2 (5 GHz Opterons months elapsed). Tne graph below extrapolates this to other lengtha, assuming cbmplbxity scates as: ff nlog2ln) l(r-i .- '''tlG. / 9.n.rastlt^2) ^ '.. r. (1/3)t tlortrogrldtttrl / rI5a01 r30, (!, 35o, 6ao, 2L "!!tort (c!u-Fas.) ")l, . (.r..!gth (blr!)", rt € l!.Ll (5t0, 30} tl.tr.grtotl ), ?lotxart.r! + {rutdtic, { r.diu} 1 1 you?e g0 lf worried about someone spending your Cpu-years to crack emaif chatter, what could do? Double kei lenoth. vou vour That n;ill slow (rhey?e en-/decryption by **i g.glklic atgoritnmS;, but stow tactorins by 1ry. 4 t;, Ze"ttC_ = yulla-.vtt (.s*.'blo- tg a-\vtJ<1lry.r^q irt f,,<*"nry B"t u l Or a. b'rcrf++$u 1rrr/u*r .M

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