The Solovay–strassen Test
نویسنده
چکیده
The Jacobi symbol satisfies many formulas that the Legendre symbol does, such as these: for a, b ∈ Z and odd m,n ∈ Z+, (1) a ≡ b mod n⇒ ( a n) = ( b n), (2) ( n ) = ( a n)( b n), (3) (−1 n ) = (−1) (n−1)/2 and ( 2 n) = (−1) (n2−1)/8, (4) ( n m) = (−1) (n ). But there is one basic rule about Legendre symbols that is not listed above for the Jacobi symbol: an analogue of Euler’s congruence a(p−1)/2 ≡ (ap ) mod p if 1 ≤ a ≤ p − 1. The natural analogue of this for an odd composite modulus n would be
منابع مشابه
Notes on Public Key Cryptography And Primality Testing Part 1: Randomized Algorithms Miller–Rabin and Solovay–Strassen Tests
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