I

r4

-1

—I

—--—I—I—

]4

‘I’

“U

I—

tU

L_L

2

__

_

II_J_

_i__

I__

I_

J_

—

-—

-

oó

I

ii-

HW

jmr

Jr6

Irt-

1HtH

1go

-4;V

pI

InH

a-

0CI

i2C)

u)

2I

__

43

I.-’

ot

C£

a.ra6

LrtJs _J

•tAtre enenly, Cl 6ncl i

_________

5

Sian C1 t (5rrn.yt)

C “a’?)tn pmcL4ci c1. c. = (5el.s

*:i

rp*0ctç\treck3 yfeUs anr pnckkc.t Oc p4;e)ch -

Catt rnMl44injy

re_rqnãcmtIe> cvcsyp#tn. I4

IME &tEik

-

-—-,:- - _— -- —

Ttjeortxn h: FIL El &aw1 cssewi..nttc4setiti& r

I zTh4oekin4&

- - 1 -‘—2---—t------——---1---1--1--*—-—-—t 4 -t- -

--•---•- ------

:

øtbnn4tc $ec4r;-y m nol be eho4,’s r strnt opphzcimns.

6, .l cs yY11le4’oie:

,Wen (k m.yt

ik’ S tc4yto pmJce ECant (5’<I(z.rn)myk)

-tsr.--

-

Pt I tt

I(ço*t ti.t txcitJesmc1ei)dy..)

.‘3wtccfia seturt’ (ACCA secut $CLLI’Ct

t.JDCOA SecwtJQ4n we Sqi.v r symnwfrt nc

s iv $eniqn secw3 e*øp- .4

tt cLtryj*on arqL\t, f;o4

H liqs Pk Sc it encyjoimn ontltmvn4+enj

(A beftrt, mqy nof &ô’e oqicic 4t kcrypt

C.k4)fl13t cirJhtrttxtàVrrr, t’,qess

—

“— —-1+ --Jc•----_--z-----___--t-_ —-;—— —-— I——-—----—-4---- —

— I —-— —

- : 1- b -

I -+

£ I +

L ____i1 L I 1 ___

—-—-

-,-.—

—---

4_i—

-_-—

c---’---

—a

—--—

---•---

r--

-t-

-1----

-$4

—-:---i-E

r-4

-

If—-

V-r

UIio

--3

t*-t

-

in

IIC

•a

ap

-

‘p20C

---f--- --H-

--

-—

-

Ifl

IHI

t_Iii

pit:,

-

t:.

-I1C

--‘if--- .—----- -——------ ——-—-----,—

_______________

-

- ....,_ - r.- _-

—

— b ‘‘t,ir ii- L..t. II

mif1 -— -- r-wt -*-,--n-- ,-- -t-- - - -- -*.- - - -.

•Crawer— c’Io4f mtii0J is su;’ F

• I..et % oerv’4p a4 pnre 0r’Ltg0 4(e.. 3 Jtt pr;pI,pt prçme’). -

—

4A_

R HXijX;ijYa, -T-- L

-1t-- 1_--viyai. -- -:

H--- r ±-- - ,-

.. .L.. _•.. -.

h -‘ .L. --:-.

Lkfl41sk

sk=

1I—

—-—:-——i—---

H 1 - . S II -I--I ,— L

£ ‘-f----J----4

- I I 3- -

1—

- H LI i —

-1— II— f

I I ,:-‘:,::4

f—j H-H-f—-H-I —I----— -i-f J_I

I — f--L-L- -I I—

L-L

.L.LL.jjJ.L ..L.:.

--

—-

‘

-::>

--—

--:

4

‘—1I-

-:

iift

ci

-

—‘iC

iii

j0

—_

_‘J

-

t

-1-

C’

r-i

-—

,ZA;

-ztR

-..

+_t:l__C

!J

‘C5

t’tjj

5H

a“

-t—

_;

7-----;--

—•••-t---i

‘.J

ç•6N

z.:

•-

••—

3ii

•c.

-H

-0j

33

I-

.4

-i-•

.4

-M0.

{if

----t.4----j----j

I

I

fI

-——

Hi

--•

-_4

c4_

(‘1

w—

——

j-—---—4--

.

-

Si

f--lri

---

c..!

.4•

,.—..

••••

•I

4‘U

-0

1-

-‘

-‘

*-‘

—‘

4-

•&I

,4•

1_i

•••—

,Lh

-‘

•-1

-t

j-,4

:1L’—

’•It

L‘A

-(•_._I,_______p

ti—-i—

i•?s>

4

a

I.-

__flt__j ——IUNDER

-

L*._i_ —---r—— I--— J

I—I—--- ,j -

rJr— -t_ -r-

II I I. —IIi 1 —r-’[ I—---- -r -—-— —

I I

- —— -‘ - -

-r —

rt’+m — i- -r -‘ -“--f--j-—t—.

I4—’

- _E_4-- - —J

I

—rt-- — F— — — - -

— r_: -I--

___

I I --—i—-

1 t -—-——1 + r-’ -1—,It I ‘

_____

— _L_ —

-F-

: -I

-

t tk ‘

Aqdc%T 444pwscvloja -I---’I I I

‘—mr-I——1-- t—- — ---u

__

--

l1eYniqn nio44 of PX e pito1 (\P7\ -

•

key, secnt ley rnes$me. S4ct, cip1w4tx4-sp.ct)

lMj:Ij.

e S(M<,.) is onefcc;enty cpwkmIe -

one-t-oa (ae¼rrn;nsh) nwp 4nm P1 4* C

- C: E (Pkçm’) ‘, (wnce) thnh*tr rn

. ‘p (sx,4)

effrc;entiy cowip%Sk inV’ttS4 ‘.

p(si<c’): D(XdIB (PK,mt= it (VmLM’)

• rt Is 4ar4jiSeosic It atrypt w

o PK hut w44,ou4 L04-tcige é 5K. -

- 5k teprtw$’c “frud” i’vStrrw$cbn tct- -

ØatS myers ion of tLic (‘ tktrwe. 9nt_was,i’

-— - - j

-4

r

- fLknchDv t(1ç.) -

t --- - --

-

- b

¶--- -- r- ;--

- --

t +--,

-

—--

A — L

ri

‘p.

Z)C

-L_i

----

-LII

itH

H-

I-ii

,r

2?

oH

kR

cttt

‘ at

DD

1n‘.

.,.1

‘S

t%

—r.

?,

-v.l-_,I pIP

11o

:,

a£

III

3 —4-—

’

tc

EJ:

KYtm 13

ci

0

Ft oI.

.fl

15c 1!9-

g*-ç

3II

;—‘

-c‘T

’1-

2±

gt

3.3

.rm

-

tve.

t

afb

rnt

9—

s>

H.4

.fl.

..:_—g

.÷

.-

q.1

a r-,

flS

A“-—

Lb gI;

4

Ii

14

i

1

I.

I H

- 4ørre4nesof RSA’..

Jsemms : -

ccrrec4recs nioA n.

Cocrec%tcs RsA MEacfl

- CmeY =Yn mE

- — —--

I -

-

- I

-

- LI,.q

€tma;nAr *wntfll or CR1)

wkert p, art cs4;nc+ primes,

]‘ven £

-

-- ‘&44H )x:y&cäpx:y(MoJ’Y

tws + swffire5 tt peon eoveecf ccl p; tke.

-&-#: rno4 ft ‘ta Sqrnt1 c’4 C1 ‘r4e bnpkes

e.4=1

so(bCl Y(n)”)

€‘a

= t (0a -t

[a:. “(4 Y(n)53

son,e-t

-

[Ac’ fr.a

By LRT we only V\etcI 40/u-fl) —m (rno4 ,“)

Pflvt

-- 6r aft n’cePI

Wt ccnstatr two caseS:

Lit. S

msO (vnSp’i

Trwt.\; O•

,Aert tAt

Iff I

fleck

]l1es (.VrnG

/ o-\’= m’(rn’ 1‘I

= n.j

(mod p’)

‘) D(5K,E(?kjvnt:n

-j —. I

Coal :

SQ

-r1’en

rn :j

e4

[rermot)

tm# (4. (p.O

(noJp

‘S

QhcI

m tm&neJpN ;r4lImt%

cm (moi ) fpr qfl n’€’t5 &;m;)arIy’

rnA tm (ma n aiim €‘Er (‘ cRy-’)

nt&

I’ I t 6rd

()

src4

7L

_

5C-

’.cC

Vt‘-•

it

‘4

‘I’

‘,•

4c’

-,

t*i

—Is

n—

Ic

c•

at

\C.

a—

•

a’i

‘-

Lt1

HM

..,S

•°

fl_

Ia

“3

p‘

I••

I t-c

Li

ccS

N

9

IS

V’

•

-.

2’

C—

4rS

6—

a,

*

;?

t.

ra

a.1

C

I

4-

4.1U‘I,

‘a

U’.a

4

-I-4

-4.4

L1

.1

.4.--

-

.

HC

V.0-oC1

4:

.a.-.

a.

1tIII

C.

.SL

-j

—-0

-C

S

i_os

*10

—

4-rr

-

%‘S

I

S

ZII0,

•.

‘I

0-

‘Lu

1450F‘AC

.

•1

IIj

S

04Ca-

-

£C

rtH.i’i

—.1

Lb

I441

0

4--t0€

-.

--1

I.1-

iI

.1:1

L

Ct‘C0

‘I

a.*

p1

I-’.

—

.*_i.-.S,—_1—

—-pb—a---—,-—--1

a...’L...

--.-S---..----

Ii.-

-

-—,-t

--

(t“r°‘4’t’’°i‘r’W&Ø‘4j4fl)

‘VP”dVO

1.avoJO?c‘Øsirnra*tow

‘3.d(1M40‘iiCng)

t4ndui‘°r 3

a.t 1t’

3k,-‘.2JO}tA4QCviAAhc,D%jrr4

---

:flQ.’4-”%158fl&noa4j

--;--

0S-ï$

r-‘IctA

I ‘S

nC

4

ICaCV-‘5

n—SC

,3%

1IIta

a‘IWI

C

ata6•IIj

ii4I

I—LiFI

I,

&C.

U

4-.0C3

14jI

—

F

•..,,

..—

.,..—1’

.

‘‘-4-

.4aCL412&

‘SC

1-‘a

3’1’ aS2

.C,

a.

a