Summary and Relationships Between Our Number Theory Tools

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Summary and Relationships Between Our Number
Theory Tools

• Network Security
• Gene Itkis

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Inverse in ZN Given N, x Find y, such
that y x mod N1 (use xGCD algorithm)
CRT2 Given N1, N2, x1, x2 Find y, such
that y mod N1x1 y mod N2x2
SQRT (for primes) Given p, y Find x,
such that x2 mod py For Blum primes
xy(p1)/4 mod p
y x1 c2 N2 x2 c1 N1 , where c1N1
mod N2 1 c2N2 mod N1 1
SQRT (for npq) Given npq, p, q, y Find
x, such that x2 mod ny Use x2 ? y (mod p) x2
? y (mod q)