IWM[\K W K IBWC T
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7/27/2019 Faulty RSA Encryption
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IWM[\K
W KIBWC T
S k d a f j d b e W k p m r t
D I { 2 : : 9 / 1
[ D E D r y p t m I r m u p S k d a f j d b e W k p m r t T k r j k s
a t t p 8 / / w w w . c j d k . u d e . b d . g k / d r y p t m /
\ e b d k c u E k v b f t , 4
G - 2 4 3 1 E m u v b j f - e b - F k u v k , G k e i j u `
\ a m f k 8 ( + 4 7 ) 2 < 3 9 7 ; 3 2
O b x 8 ( + 4 7 ) 2 < 3 9 7 ; : 1
O b u e t y W T B k f d r y p t j m f
@ . H m y k b f c H . - H . R u j s q u b t k r
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O b u e t y W T B k f d r y p t j m f
@ . H m y k b f c H . - H . R u j s q u b t k r
H u e y 7 3 , 2 : : 9
C k p b r t k ` k f t c '
K e k d t r j d j t k ( C J D K ) , [ f j v k r s j t k d b t a m e j q u k c k E m u v b j f
\ e b d k c u E k v b f t , 4 , G - 2 4 3 1 E m u v b j f - e b - F k u v k , G k e i j u `
K ` b j e 8 o h m y k , h h q i L c j d k . u d e . b d . g k
B g s t r b d t . S a k b u t a m r s s a m w t a b t t a k p r k s k f d k m o t r b f s j k f t o b u e t s j s
c b f i k r m u s w a k f k f d r y p t j f i ` k s s b i k s w j t a t a k W T B d r y p t m s y s t k ` . J f
p b r t j d u e b r , t a k y s a m w a m w b d r y p t b f b e y s t d b f r k d m v k r b p e b j f t k x t w j t a -
m u t n f m w j f i t a k s k d r k t p b r b ` k t k r s .
2 J f t r m c u d t j m f
T j ` ` m f s p m j f t k c m u t j f 2 P t a b t t a k u s k m o b d m ` ` m f W T B 7 P ` m c u e u s j s
c b f i k r m u s . J f c k k c , j o t a k s b ` k ` k s s b i k ̀ j s k f d r y p t k c w j t a d m p r j ` k p u g e j d
k f d r y p t j m f n k y s k
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r k d m v k r b p e b j f t k x t j f t a k p r k s k f d k m o t r b f s j k f t o b u e t s .
7 O b u e t y W T B k f d r y p t j m f
Y k s u p p m s k t a b t b f k r r m r m d d u r s c u r j f i t a k d m ` p u t b t j m f m o t a k d j p a k r t k x t .
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t a
g j t m o k j p s t m j t s d m ` p e k ` k f t b r y v b e u k .
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D I { 2 : : 9 / 1
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2 : : 9 g y [ D E D r y p t m I r m u p
O m r ` m r k j f o m r ` b t j m f s , s k k
a t t p 8 / / w w w . c j d k . u d e . b d . g k / d r y p t m / t k d a r k p m r t s . a t ` e
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O b u e t y W T B k f d r y p t j m f 7
E k t 0 i d c ( V k > k ) . T j f d k 0 i d c ( k 7
h
> k ) , c j v j c k s 7
h
. S a j s j ` p e j k s
0 2 g k d b u s k k j s m c c j f t a k W T B d r y p t m s y s t k ` . D m f s k q u k f t e y , t a k ` k s s b i k
̀ d b f g k r k d m v k r k c o r m ` d b f c V d g y t a k d m ` ` m f ` m c u e u s b t t b d n p r k v j m u s e y
c k s d r j g k c .
4 K x t k f s j m f t m m t a k r s y s t k ` s
B o t k r j t s j f t r m c u d t j m f j f 2 : 9 1 , t a k W T B d r y p t m s y s t k ` w b s k x t k f c k c t m E u d b s
s k q u k f d k s t m p r m c u d k E [ D 4 P . J t w b s b e s m k x t k f c k c t m k e e j p t j d d u r v k s g y
N m y b ` b , @ b u r k r , M n b ` m t m b f c _ b f s t m f k , t a k s m - d b e e k c N @ M _ d r y p t m s y s -
t k ` 3 P , b f c e b t k r g y C k ` y t n m ; P .
N @ M _ j s a m ` m ` m r p a j d b f c j s t a k r k o m r k s u s d k p t j g e k t m t a k d m ` ` m f ` m c -
u e u s b t t b d n . E [ D b f c t a k C k ` y t n m ' s s y s t k ` b p p b r k f t e y s k k ` t m g k r k s j s t b f t
g k d b u s k t a k j r f m f - a m ` m ` m r p a j d f b t u r k . A m w k v k r , G e k j d a k f g b d a k r , H m y k b f c
R u j s q u b t k r ? P r k d k f t e y k x a j g j t k c b d a m s k f - ` k s s b i k r k q u j r j f i m f e y m f k ` k s -
s b i k b i b j f s t E [ D b f c t a k C k ` y t n m ' s s y s t k ` . T m , t a k s k e b t t k r s y s t k ` s b r k
b e s m v u e f k r b g e k t m t a k d m ` ` m f ` m c u e u s b t t b d n . O m r E [ D b f c N @ M _ , t a k
k f d r y p t j m f n k y k ` u s t g k m c c > t a k r k o m r k t a k d m f c j t j m f i d c ( V k > k ) 0 2 j s b e w b y s
s b t j s k c . S a j s j s f m t f k d k s s b r j e y t a k d b s k o m r t a k C k ` y t n m ' s s y s t k ` .
Y a k f s k v k r b e g j t s m o t a k k f d r y p t j m f k x p m f k f t j p , t a k b t t b d n ` b y s t j e e
b p p e y m r f m t c k p k f c j f i m f t a k v b e u k m o i d c ( V k > k ) . F m t k b e s m t a b t u s j f i p r j ` k
p u g e j d k f d r y p t j m f k x p m f k f t s j s c b f i k r m u s g k d b u s k , j f t a b t d b s k , t a k b t t b d n j s
b e w b y s b p p e j d b g e k .
W k o k r k f d k s
2 P s j ` ` m f s , i . h . 8 l B l w k b n ' p r j v b d y p r m t m d m e u s j f i t a k W T B d r y p t m b e i m -
r j t a ` ' , D r y p t m e m i j b , ( B p r . 2 : 1 4 ) , 9 , ( 7 ) , 2 1 < { 2 1 7
7 P r j v k s t , r . e . , s a b ` j r , b . , b f c b c e k ` b f , e . 8 l B ` k t a m c o m r m g t b j f j f i
c j i j t b e s j i f b t u r k s b f c p u g e j d - n k y d r y p t m s y s t k ` s ' , D m ` ` u f j d b t j m f s m o t a k
B D @ , ( O k g . 2 : 9 1 ) , 7 2 , ( 7 ) , 2 7 < { 2 7 ? .
4 P s ` j t a , p . h . , b f c e k f f m f , ` . h . h . 8 l E [ D 8 B f k w p u g e j d n k y s y s t k ` ' ,
j f F j f t a J O J \ T y ` p m s j u ` m f D m ` p u t k r T k d u r j t y ( 2 : : 4 ) , K e s k v j k r T d j k f d k
\ u g e j s a k r s , p p . 2 < 4 { 2 2 9 .
3 P n m y b ` b , n . , ` b u r k r , u . ` . , m n b ` m t m , t . , b f c v b f s t m f k , s . b . 8
l F k w p u g e j d - n k y s d a k ` k s g b s k c m f k e e j p t j d d u r v k s m v k r t a k r j f i X X
f
' , j f
B c v b f d k j f D r y p t m e m i y { D r y p t m ' : 2 ( 2 : : 7 ) , v m e . ; 9 ? m o E k d t u r k s F m t k s j f
D m ` p u t k r T d j k f d k , T p r j f i k r - _ k r e b i , p p . 7 ; 7 { 7 ? ? .
D I { 2 : : 9 / 1
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O b u e t y W T B k f d r y p t j m f 4
; P c k ` y t n m , f . 8 l B f k w k e e j p t j d d u r v k g b s k c b f b e m i u k m o W T B ' , j f B c -
v b f d k j f D r y p t m e m i y { K u r m d r y p t ' : 4 ( 2 : : 3 ) , v m e . 9 ? ; m o E k d t u r k s F m t k s j f
D m ` p u t k r T d j k f d k , T p r j f i k r - _ k r e b i , p p . 3 < { 3 : .
? P g e k j d a k f g b d a k r , c . , h m y k , ` . , b f c q u j s q u b t k r , h . - h . 8 l B f k w b f c
m p t j ` b e d a m s k f ` k s s b i k b t t b d n m f W T B - t y p k d r y p t m s y s t k ` s ' , j f J f o m r ` b -
t j m f b f c D m ` ` u f j d b t j m f s T k d u r j t y ( 2 : : 9 ) , v m e . 2 4 4 3 m o E k d t u r k s F m t k s j f
D m ` p u t k r T d j k f d k , T p r j f i k r - _ k r e b i , p p . 4 < 7 { 4 2 4 .
D I { 2 : : 9 / 1
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