Post Quantum Crypto B e r n d F i x < b r f @ h o - PowerPoint PPT Presentation

1 / 2 9 Post Quantum Crypto B e r n d F i x < b r f @ h o i - p o l l o i . o r g > Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

2 / 2 9 Intro „ P r o p e r l y i m p l e m e n t e d s t r o n g E n c r y p t i o n w o r k s . c r y p t o s y s t e m s a r e o n e o f t h e f e w t h i n g s t h a t y o u c a n r e l y o n . “ E d w a r d S n o w d e n Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

3 / 2 9 Intro https://cryptoparty.in t G o t o o fj n d o n e n e a r y o u . . . Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

4 / 2 9 Intro c r y p t o c a l y p s e T h e u p c o m i n g : ● M ( l i k e O p e n P G P e m a i l s ) o s t e n c r y p t e d c o mmu n i c a t i o n a n d a l o t o f t r a n s i e n t c o m m u n i c a t i o n ( w i t h S S L / T L S ) d o e s ( „ P e r f e c t F o r w a r d S e c r e c y “ ) . n o t p r o v i d e P F S ● M m i n o s t e n c r y p t e d c o mmu n i c a t i o n i s s t o r e d l o n g - t e r d a t a c e n t e r s a r o u n d t h e w o r l d b y s e c r e t a g e n c i e s ( B l u ff d a l e , i s j u s t o n e o f t h e m ) . U t a h ● M o s t p u b l i c - k e y e n c r y p t i o n s c h e me s w i l l b e b r o k e n d u e t o a d v a n c e m e n t s i n q u a n t u m w i t h i n t h e n e x t t e n y e a r s c o m p u t e r t e c h n o l o g y . Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

5 / 2 9 Intro T h i n g s w e n e e d t o s t a r t d o i n g r i g h t : N O W ● O : n l y u s e P F S c r y p t o s c h e me s w h e n c o mmu n i c a t i n g o n l i n e G e t r i d o f O p e n P G P e m a i l a n d m o v e t o s y s t e m s l i k e P o n d ( h t t p s : / / p o n d . i m p e r i a l v i o l e t . o r g / ) . F i x t h e S S L / T L S s e t t i n g s o n y o u r o w n s e r v e r s a n d / o r k i c k a s s w i t h o p e r a t o r s . S t o p u s i n g s e r v i c e s t h a t d o n ' t c a r e t o c o m p l y . ● D e s i g n , i mp l e me n t a n d d e p l o y n e w p u b l i c - k e y c r y p t o s c h e me s t h a t c a n n o t b e b r o k e n b y q u a n t u m c o mp u t e r s Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

6 / 2 9 Table of Contents ● E x i s t i n g a s y m m e t r i c k e y a l g o r i t h m s ( p u b l i c k e y c r y p t o s ) ● A t t a c k v e c t o r s o n p u b l i c k e y c r y p t o s ● C l a s s i c a l a p p r o a c h ● Q u a n t u m c o m p u t i n g ● Q u a n t u m - r e s i s t e n t p u b l i c k e y c r y p t o s ● L a t t i c e - b a s e d c r y p t o ● C r y p t o s b a s e s o n e n c o d i n g p r o b l e m s Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

7 / 2 9 RSA algorithm (1977) m = p ⋅ q r c a n o n l y b e c o m p u t e d w i t h r : = ϕ( m ) = ( p − 1 )⋅( q − 1 ) p , q ) k n o w l e d g e o f ( n ⋅ r + 1 ≡ g ( mod m ) d ⋅ e ≡ g g ⇒ e d : a p u b l i c e x p o n e n t a n d a p r i v a t e e x p o n e n t C h o o s e c o m p u t e − 1 ( mod r ) d = e d ⋅ e ≡ 1 ( mod r ) ⇒ e , m ) : ( P u b l i c k e y d , m ) : ( P r i v a t e k e y Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

8 / 2 9 RSA algorithm (1977) ( D L P : D i s c r e t e L o g a r i t h m P r o b l e m ) ● Encryption : ● Signature : e mod m d mod m b = a b = a ● Decryption : ● Verifjcation : d ≡ a e ≡ a e ⋅ d mod m = a d ⋅ e mod m = a b b Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

9 / 2 9 Elliptic Curve Crypto (1985) 2 = x 3 + a ⋅ x + b ( mod p ) y Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

1 0 / 2 9 Elliptic Curve Crypto (1985) 〈 G 〉 F G G e n e r a t o r p o i n t f o r m s a n a d d i t i v e c y c l i c g r o u p o n c u r v e p ∞ n G n ⋅ G T h e o r d e r o f o n t h e c u r v e i s t h e s m a l l e s t v a l u e w i t h = = ⋅ G P a a (mod n) ⇒ a l l p o i n t s o n t h e c u r v e h a v e t h e f o r m w i t h s c a l a r P = a ⋅ G , I t i s e a s y t o c o m p u t e a P G b u t „ i n f e a s i b l e “ t o c o m p u t e f r o m a n d ( a n a l o g t o D L P : D i s c r e t e L o g a r i t h m P r o b l e m , b u t m u c h m o r e d i ffj c u l t t o s o l v e t h a n D L P o v e r fj n i t e fj e l d s ⇒ s h o r t e r k e y s ) Private key: d Public key: d ⋅ G Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

1 1 / 2 9 Elliptic Curve Crypto (1985) E v e r y D L P - b a s e d c r y p t o s y s t e m ( D S A , E l G a m a l , D H ) c a n b e t r a n s f o r m e d i n t o a n E C C - b a s e d c r y p t o s y s t e m ! ● Signature / Verifjcation: E C D S A ● En-/Decryption: E C D H DH (Diffje-Hellman) ECDH ● P ● P g , p G , n a r a m e t e r a r a m e t e r ● R d A d B ● R d A d B a n d o m s e c r e t s : a n d a n d o m s e c r e t s : a n d d X mod p ● P ● P e X = d X ⋅ G mod n e X = g u b l i c : u b l i c : d B = e B d A ( mod p ) ● S ● S s = e A S = e A ⋅ d B = e B ⋅ d A ( mod n ) h a r e d : h a r e d : Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

1 2 / 2 9 Attack vectors Classical approach (number theory): e ( mod m ) a = b ● Discrete Logarithm Problem: [ R S A ] P = a ⋅ G ( mod n ) [ E C C ] Pollard-Rho algorithm, Baby-step giant-step m = p ⋅ q ● Integer Factorization: [ R S A ] All forms of quadratic sieves to fjnd congruences a 2 b 2 mod m ) ≡ ( p = ( a + b ) , q = ( a − b ) 2 − b 2 ⇒ m = p ⋅ q =( a + b ) ⋅ ( a − b )= a 2 ≡ b 2 ( mod m ) ⇒ a Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

1 3 / 2 9 Attack vectors Quantum computing (1994) Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

1 4 / 2 9 Quantum computers Qubits: : α ∣ 0 〉 + β ∣ 1 〉 = α ( 0 ) + β ( 1 ) 1 0 ● T w o s t a t e s i n s u p e r p o s i t i o n ● R Josephson junctions , e a l i z e d w i t h i o n t r a p s , N M R , p h o t o n s , . . . T w o s u p e r c o n d u c t i n g r e g i o n s ( l o o p ) s e p a r a t e d b y a w e a k l i n k ( i n s u l a t o r ) S Q U I D ( u s e d f o r r e a d - o u t ) S o u r c e : e n . w i k i p e d i a . o r g Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >

1 5 / 2 9 Quantum computers Qubits (Josephson junction): ● Writing : A p p l y a m a g n e t i c fj e l d , c u r r e n t s w i l l fm o w i n t h e l o o p A p p l y a m a g n e t i c fj e l d a n d t h e g r o u n d p a r t i c u l a r s t a t e i s s p l i t i n t o t w o s t a t e s i n s u p e r p o s i t i o n . ∣ 1 〉 ∣ 0 〉 ● Reading : U s e a s q u i d t o m e a s u r e t h e fm o w s i n t h e l o o p Post-Quantum Crypto Bernd Fix < b r f @ h o i - p o l l o i . o r g >