PRBGs Pseudorandom Bit Generators

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PRBGs Pseudo-random Bit Generators
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????

• ????? ??????? ????????? ????? ????? ?? ?????
• ???????????.
• RSA , DES , Digital Signature ) ????... (.
• ????? ????? ?? probability-based searching
  strategy.
• ?? ????? .
• ????? ?????????? Pseudo-Random bit Generator
  ?????? ??????.

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ANSI X9.17

• ????? ?-generator ??? ???? ?????????? , ??????
• Triple DES, ?????? ??????? ??????? ?????, PGP .
• ????? ??? ????? ?????? ?????? , ????? 64 ?????.
• 1. DTi - ???? ?? ???? ?????? ??????? ?????? ??
  ??? i .
• 2. Vi seed (?????) ?????? ???????? ???????
  ?????
• ????? ?- generation .

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ANSI X9.17

• Keys k1,k2 ????? 56 ????? ?? ???, ????????.
• ?- Generator ????? ?- 3 ?????? ?? ????? ???
  Triple DES
• ??????? ?????? ?????? ??????? , ???????? ??? ??
  ??? ?????? pseudo random generation .
• ????? Ri , Vi1
• Ri ???? pseudo random
• ( ??????? ??"? ?- generator ) , ????? ??? ??????
  ????? Vi1
• 2. Vi1 seed value ?????? ?????? ?? -
  generation.

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ANSI X9.17
K1,K2
K1,K2
K1,K2
DTi
EDE
Vi1
EDE
Vi
EDE
Ri
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ANSI X9.17

• ?????? ??????? ????? ?????? ?????? ?- generator
  
• ??????? ??????? 2 ?????? ????? 56 ????? ?? ??? ,
  ?-3 ?????? ?? EDE (Encryption-Decryption-Encryptio
  n)
• ?????? ?? ??? ??????.
• ????? ????? ?? Ri , ?? ???? ?????? ????? Vi1 ,
  ?????? ????? ??? EDE , ?????? ???????.

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Linear Congruential Generator

• ???? ?????????
• ??? ????? ????????
• ????? m gt2
• a,b ???????? -
• ????? k

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Linear Congruential Generator

• ????? t ?????
• ????? s0 ?- sequence ????? lt m-1 s0 0 lt
• ???? t ???????? ????? ????? ????.

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Linear Congruential Generator

• ??? ?- Sequence ?"? si (a.si-1 b) mod m
  

3. ???? 1 lt i lt t
???? zi ???? ?- least significant bit ?? si .
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Linear Congruential Generator

• ????? ???? m16, a5, b5, s07
• S1 (5.75)mod16 8
• S2 (5.85)mod16 13
• .
• ????? 7,8,13,6,3,4,9,2,15,0,5,14,11,12,1,10,7,8,
  13,6,3,
• k log2m 4 , k1 lt t ltm1 t 6
  
• ????? f(7)
  0,1,0,1,0,1,

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Linear Congruential Generator

• ????? ??-sequence ?? ????????
• ????? ?? ?????? ???? zi ( mod 2 si) ?????
  ????? ??????? ?? ????? ????? t.
• ???? ?????? f(s0) , ????
• (k,t)-Linear Congruential Generator

???????...
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Linear Congruential Generator

• ????? ????????? ?? ????? ??? ?????? ????????, ??
  ?? ????? ????
• ???? ????????? ???????,
• ??? ?? ????? ????? ???????????.

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RSA Generator

• ??? ??? ?????? ?????? ???????? p , q.
• ????? k/2 .

• n p.q
• ??? ???? ????? b ???? ?????
• ???? n , b Public Keys
• p , q Private Keys

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RSA Generator

• ???? s0 - seed ???? ???????? ????? 1 , n-1.
• s0 ??? k ?????.
• ???? i gt1 ?????
• zi ???? ??? ?????? ?????? ??????? ??"? ?????
  i.
• 4. ???? ??? ?? ????? ?- output
• ????? ????? ????????.

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RSA Generator

• ????? ?-generator ???? ???? ???? ????
• ?????? RSA .
• ??? ?- n ???? ???? ???? ( p , q ?????? ????????
  ??????)
• ??? ?- generator ???? ???? ????.

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????? ?? RSA Generator

• ?????? ?????? ?????? ?"? ???? ???? ?? RSA
• Micalli Shnorr pseudo random bit generator.
• ?????
• ??? p , q ????????.
• n p.q. ????
• ???? ?? ???? ?????? ?? n
• ????? ?????? Nfloor(lgn)1

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????? ?? RSA Generator

• ??? ???? ??? b ?????? ?? ?????
• ???????
• ??? k ?? ?-

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????? ?? RSA Generator

• 2. ???? s0 - seed ???? ???????? ????? 1 ,
  r-1.
• s0 ??? r ?????.
• 3. ???? i1 to t
• 4. ??????? ?? ??????
• ????? kt

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????? ???????
? RSA ?? k ????? , ???????? ?? ????? ???? ???
???? ?????? ???, ??? ????????? Micalli ?? r ?????
?????? ??????.
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BBS Generator Quadratic Residue

• ???? ?"? Blum , Blum-Shub
• ??? ???????? ????? ???? ?- RSA .
• ??? ??? ????? ?? ????? Quadratic residues ??
  ?????? ??????? ?? n ?? ????.

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BBS Generator Quadratic Residue

• ??? ??? ?????? ???????? p , q. ????? k/2 .
• ????
• p q 3 mod 4
• n p.q
• ???? n , b Public Keys
• p , q Private Keys

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BBS Generator Quadratic Residue
2. ??? QR(n)
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BBS Generator Quadratic Residue

• ???? s0 - seed ???? ???????? ????? ?? QR(n) .
• ????? si2 mod n si1
• si mod 2 zi

• zi ???? ??? ?????? ?????? ??????? ??"? ?????
  i.
• 4. ???? ??? ?? ????? ?- output
• ????? ????? ????????.

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BBS Generator Quadratic Residue

• ????? ?????? ?????? ????? z1,z2,,zt
• ???? n192649383x503 and s01013552(n) 20749

????
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BBS Security

• ?????? ?????? ?????? ???? ????? ??? ????????? ???
  ??? ????? ??????.
• ???????? ????? ??? ?- so ???? ????? ????? ????
  ??? ??? ???? ?????? ????? ?? ?????? ???????????.
• , ?? ?- QR mod n ???? ??
  ????
• ??????.

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?????

• ???? ????? ?? ????? ????? ?????? ?? ????? ??????
  pseudo ???????.
• ???? ?????? ?- generator ????? ????? ????? ??
  ???? ????.