2. Date
Page
STUDYBUDOIES
Thapdaa fuundisnauá8p.teialdaa
sasassat-way
kunEen ane widl adn publik-k.ecYptogaph
3
Ln)
Snfonomally,a functieof:io,13 xfo,1 1o,13.m(n)
tapdoo
mln)
-3t _a niua netan
Rtm)
-Bfinsd pubtie ke t0,1}, f.y) isveAas
ncen o hat maps m hits zo min) bit. Then
an eKtcat_alaou thm that o jnput
( , 2 preducs a Sneh tha a )=4
napiesn ky zeio,1
Given M and 4M),itis hand o find a mssaag MEM1
Auch hat f(M') f(M)
c t ar
3RSA
a) p-3,9 ll, ee1,M:5
px 33 bay m)=(p-1)x(2-1)E20-
ed med hlnE1
7d moo 20 1
Einling d sing
e r t e n d e d e L c l i d e a a s algchthm,
Pobile key (33,1)
cello
3. Dete J
STUDYBUDDIES
ST S
t at,-qt
1 0 0 2
20
-1 2
6 6L 1 - 1 -20
10
-
Pruvat ka 33,3)
Encyptioni E M mod m
(5) midk 33
78125 mod 33
E14 A
*Decnaptien D =t mod m
(14 med 33
2744 mod 33
D 5
p=5,ql, :3,MM:9
(n) =Ho
Foblc key (55,3)
pln)=
3d ma 55 1
9ed mod
celio
4. Date
Page
STUDYBUDDIES
1S S Ss
18 553- O 10
1 1-18
3 1 -01 3 - 18
55
3
- -18 5g
Td-t meq ative
d 55-18
d 31
Pate ke (55,31)
KEncu ptien E =M ood
CE() mol55
729 mod 55
becn ptieni D C
(I4)O med 55
p l , q-1l, e 1, M:8
Pubc ki (71,t)
I7d mod 60 1
i cellob
5. Date
Fage
STUDY BUDDIES
2 t
S
6o17 9 0 1 O 3
1789 8 1 I-3 4
1 8 2 -3t4 - 7
8 O 9i- 2 171 -7 Co
10 - 17
re
rrd =60T
a53
Pris keq (17,55
Xtncuptien E: M mod n
7
(8) mod 17
Dechpien i-De E mod m
(51)° mod 11
D8
np 4
n) (n-1)KCp-1) =2o
Pubi kea (u3,11)
ed mod pln):
Ild mod 12o 1
Cello
6. Dute
hge
STUDY BUuDDIES
2
o120 111o o J-10
L221110 1o11
0101 c-1 1 0 12o
-10
o8
ral-Pvats ky (143,1)
Enchypen i-E M n
106
& Decw
106) mad 143
D 1
e) p 11q 31, e=1 M:2
m:pxq 527,ln): (p-)XC ) L80
Pubtie key (527,1)
ed ood Cn2:1
1d mod h8o 1
cello
7. pete
Page
STUDY BuDDIES
t
1 1 0 ci-68
7 43 0 1
3 1 1 2 -69 69 13
3 3 1 0 2 7 69 -137480
-197480
L waid 80 -131
En ption E= Mm.od
(a)mad 52
E129
Dechustien E ed n
L3S) (129)34 med 527
D
u)e 31
m=3599. -
Hunc d 2zo find t paimi factoA n
Usinq tai and ho pimfactoYs
ane 59, 61
cello
8. Date
Page
STUDYBUoDIES]
m3519 GLX 5
P 54261La oiaitl
mPXxq slm) (p-1)XCa-1) 58x60 3483o
ed mod
31d m od L480=
312 348D 31 -112
31, 8 1
A 112 337
8 7o 11 -3 -112 337-44
31 337-449 3480
-
4 31
d 3480 -44
d 303)
Pvats ke (359,3031)
XMudipticatiye Jnves 3l_mod fm)
,
3480
Cello
9. Date J
fage
STUDYBUDDIES
can)
AperfoLmtdin abau
A tep,t Eateided Eueid
multi plieatiut invA 31 a 303
Db Helloman key Erehang Techniqu
Pi ne',P : +1
5pimiise oos 14 e i1,ll1,13,21,
t G Cpximitive oot
USen A B
USe
Pri yak
X 5
fid ra 12
G ied P Y G mad P
(7) mod 1 (7 )2 mad
1G801 mad
13HI287201 mad
mod
Y5
Publiekes wl ba_eLchangd
Cello
10. Date
Page
STUDYBUDDIES
A
med P
4) med F2 E) (51)m od 1
k 30
A
k Shaed 30 CSecut ka)
Eigamal CpSgad
24
(6 Puelie ke Randem Inteqe,k=2
M -30
k:(Y mad. q
(3) mod 1
Cipha Tet , C,=_kXM mo q
(1x 2o)mod 1
240mod
C52
cello
12. Date
STUDY BuDDIES
Th SHe nitubndAac combination ol baaic
anthmtic and
aqiea undion to
compudsth
a
hash falui o(amLSAg.
T
básikahthmilieane egiecol funAiens uasd
Ra SHA aeluedi
Bitsta opeudtieas (AND,OR,xoR, NoTD
Thts_d iid to manplat adivinalbt
a th aALt majasa_and iteumsdiat hash
NaLus. atzlaldp
LL Adoiten medula 2 (Densted as+
dtsadA webinahqali bis,
LAnse SHAfunctis
LRteunDestRd os RoTLand ROTR"
The uAL tohdtta ths bita oaniaput
Yalae Saabl to tE REaspectivel
iw)Loseol functions CMaonity , pam chaius)
LAmain ths hts th iaeut
maAsa andLtuLmsliathashNalu a
Thi wALd to
8)Th equolen to ealculat th alu wl6,w17
wiand w1g a a follatup i
i6 ai(wis) w tcow2) twlG 00
Cello
13. pate
Pege
STUDY BUuDoIES
w gi(wn) w9tcolwiu)ti8
a n ao andol at t ethsHA-512
ag sehadul funetensi
o()= (ngktaatata) x0( ugbEatate 8) Xo
OL()=(2 ughthstati 19) Xo L iahtaatat6) Xo
ightntau
penatiens that netatiiandd t tha bnay.
and niaits a bituisa
SnapHeARrtalen h h inpt,ALApaetu
denstis adidten mmeLulp 2 and x0
oe
denstab the leituuA exelusives epetatien
Thapaddinajald bit luaeAy 895
bjs hich mako a ttal 81G lats padoung
hlangth td 1919,epaesantcd asa 12
it ea-endian iNalue
OxO0Oo o0O0 000o000o 00óoooo ooo o0 oo Oo00o 000
Pr o o0.o.00o0 ooo0o7A
cello
14. Date
Page
STUDYBUDDIES
b)192o bit
T padding tuld i bit falloweA by 8a4 'o' bit,
whichmakia tota 345 its padding
ngth ald is i920, ep 2ussatad s a128-bit
uan Vaue
OxOooooooo o00ooo0O
O0000ooo o0 00018o
c) 192 t
padding id ' btfollused 33 o bda
whih mak.e a htal 89 bs padding
The
1k nth field a 1921,nepnessnd1d_as a128-bit bi
endico valua
OxODoo0000 O000Oooo O000 oo00
o000D 181
cello
