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

▶
e
SMART_READER_LITE
LIVE PREVIEW

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

Sep 13, 2022 343 likes •441 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

slide-1
SLIDE 1

kg* ct- /cl.eV t M'rnclf6 -a c

?tl * 5a l,ila Cr utl17-? M

eqolrr44lV cv naw *V olqtl'-t

hov nrb* v?

gt-a,sb t*1h1"'7

t fn(7rl*

e

S- b4t 'e fu

  • r^t1

e t - t

slide-2
SLIDE 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 graph below extrapolates this to other lengths, assuming complexity scales as:

‰

64 9 n log2HnL

3

In[150]:= f@n_D := Exp@H64 ê 9 * n * Log@nD^2L^H1 ê 3LD

Show@LogPlot@f@nD ê f@640D * 30, 8n, 350, 640 * 2<, AxesLabel Ø 8"Length HbitsL", "Effort HCPU-yearsL"<D, ListLogPlot@88640, 30<<, PlotMarkers Ø 8Automatic, Medium<DD

Out[151]=

Ê

400 600 800 1000 1200 Length HbitsL 0.1 100 105 108 Effort HCPU-yearsL

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.

slide-3
SLIDE 3

'Eqf-640", a 640.bit (1g3-digits) number was factored in 2OO5 using gO CPU-years

  • n

a cluster

  • t

2.2 GHz Opterons (5 months elapsed). Tne graph below extrapolates this to

  • ther

lengtha, assuming cbmplbxity scates as:

'.. r. l(r-i .- '''tlG. / 9.n.rastlt^2) ^ (1/3)t tlortrogrldtttrl / rI5a01 r30, (!, 35o, 6ao, 2L rt€l!.Ll . (.r..!gth (blr!)", "!!tort (c!u-Fas.) ")l, tl.tr.grtotl { (5t0, 30} ), ?lotxart.r! + {rutdtic, r.diu} 1 1

lf you?e worried about someone spending g0 Cpu-years to crack your emaif chatter, what could vou do? Double vour kei lenoth. That n;ill slow en-/decryption by **i (rhey?e g.glklic atgoritnmS;, but stow

tactorins by 1ry. 4 t;, Ze"ttC_

=

B"t tg a-\vtJ<1lry.r^q irt f,,<*"nry yulla-.vtt (.s*.'blo-

u l

ff nlog2ln)

Or a. b'rcrf++$u 1rrr/u*r .M

slide-4
SLIDE 4

x ' 9 €(W")=

v*

. f t

,t kl

?4v (x 1 vr) *n )

i( nze v*-^ t

) = ?a.rC r, E JrnD

r tl, {.lry k;fro*-V S

  • -)

| = l- wr{ *t

i f 1 f 1 o & f l - I . {

v*..us 7

Tt'q i lnr;,.-t n

  • JrJ,

l.e/./ n

Ll'n

slide-5
SLIDE 5

Priu, ,Jr, Te>17

it U i', frar4 ( iF .*'.* t glu)

1fr;tr)

rts*''r9^

ll-(

A €

+l^

iI vr rl e&ftlfr, +e, "!:2

'"+'.*

{rr 4ra +{*,. ,.r. a} Cdirc.|A.

,1,;!: r {-rL'e1 z'*,] rJrr

n it a, Cryx. r&.,0

tf -tt| %*A,..rt aFtt @r) F-cll a

_. tU

a r ' t c . n . b < l o c

ecuToltd

Bf \rr<

a u h e f . 4 ) r / i - ^ ' l

(c.r.l ir

tlv.fu2l si

wtrrTotlu.

bt3+v*l

slide-6
SLIDE 6

i{1 trfTt

Yt= |

a y = t (

r€t $471

X 2.1@rl?)

t) uAp +f *r

  • l

T.la1,b ullr, +

1o*i.

x1, I .^lt

? \(r? t)

f i (r-r )(r+r )

QrtL P ( (r'r)

tr€(

ntz E

,r*

a a l

I

\ ,

It

(v-t c )

{*-1 ('||,Jc)

:, *1.t&,

,. p (Jt+r )

,1. X; -f (4)

at*r

slide-7
SLIDE 7

f ece,pfr-,

yl (avu, Cer;&ll

@e ^ d ert&t-

n*'* t $clv)

'L l lg r (ur l*) 4.,\

icu-# l+tttw.. h)

{wrtv.a q &*Vry

?*( 4.1 t1-t2 h ) .

@ ?.r+L'---a >, L-d

ru lgq _a h-J *4,u lotryJy.

(J0..* lr * tu 1

?fcA l*lor t

*ty tfu

il'\a,r,'}''-ll teTf g?t

a.{ r

%'Mta. v\ "? v.b[l ?vw, q 2l-e

&'t

h.l+

,7 t.

frF

f$?

slide-8
SLIDE 8

h..'l(r,;-R*llrrr ft f*f* .r4el

9rhl4 ' n,ldl v.tJ, E + \rr +fu' for hrTr );Sh*fbt7 furl,}vt* +1'*, atu,)a1s i t AteAe;lrt t b* ,,p r..,"j ,, *.1 (,.rcl" .crt*. ad* ?lcb.*hh ) alue,,lf tlr' *rle,p1Jr/g, , g*, ( n , 3 " 1 , k c f c / t % i r . r y e .

?nlo.b'(* rt

, .- flrD . Ss tA , 4rl

  • dd1url4

v qtre^ ,ir e vJ c64vd rr{t tal rlur4 ut{0. 7.rl oJl*r, ?tft al, r mt!-tr o4o 7ra urtry

hll*ulas vi.h .a3 ltelt ?qbb,lr{2,

Frr.f $f4t A d,otuvrtfit/+. *"++

!?rrrntf2@

(_Alvav41 k1a,/.1S.eq , z*z1

t{rt ,tu).t wvlrl q4,h{ St+qu go letf wz&J ,.t{ ?, ?"4*14., dig2sl* itt obttcrt *Qa'e4 dr"-jz..ivq