M. Rabin. Probabilistic algorithm for primality testing, Journal of Number Theory 12 (1980), 128--138. Home/Search Document Not in Database Summary Related Articles Check |
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Computational Methods in Public Key Cryptology - Lenstra (2001) (Correct)
.... 1 is called a witness to the compositeness of n if a u ## 1 mod n and a 2 i u ## 1 mod n for i with 0 # i t: For odd composite n and a randomly selected a # 2; 3; n 1 there is a probability of at least 75 that a is witness to the compositeness of n, as shown in [97]. It follows that in practice the compositeness of any composite n can eciently be proved: Probabilistic compositeness test Let n be an odd positive number, and let k be a positive integer. Randomly and independently select at most k values a # 2; 3; n 1 until an a is found that ....
M.O. Rabin, Probabilistic algorithms for primality testing, J. Number Theory, 12 (1980) 128-138.
A Lower Bound for Primality - Allender, Saks, Shparlinski (1999) (2 citations) (Correct)
....z Supported in part by NSF grant CCR 9700239. x Supported in part by ARC grant A69700294. 1 Introduction What is the computational complexity of the set of prime numbers There is a large body of work presenting important upper bounds on the complexity of the set of primes (including [AH87, APR83, Mil76, R80, SS77]) but as was pointed out recently in [BDS98a, BDS98b, BS99, Shp98] other than the work of [Med91, Man92] almost nothing has been published regarding lower bounds on the complexity of this set. In the context of space bounded computation, it was shown in [HS68] that at least logarithmic space ....
M. Rabin. Probabilistic algorithm for primality testing, Journal of Number Theory 12 (1980), 128--138.
A Lower Bound for Primality - Allender, Saks, al. (1999) (2 citations) (Correct)
....of square free numbers, and for the problem of computing the greatest common divisor of two numbers. 1 Introduction What is the computational complexity of the set of prime numbers There is a large body of work presenting important upper bounds on the complexity of the set of primes (including [AH87, APR83, Mil76, R80, SS77]) but Supported in part by NSF grant CCR 9734918. y Supported in part by NSF grant CCR 9700239. z Supported in part by ARC grant A69700294. as was pointed out recently in [BDS98a, BDS98b, BS99, Shp98] other than the work of [Med91, Man92] almost nothing has been published regarding ....
M. Rabin. Probabilistic algorithm for primality testing, Journal of Number Theory 12 (1980), 128--138.
A Lower Bound for Primality - Allender, Saks, Shparlinski (1999) (2 citations) (Correct)
....1 Introduction What is the computational complexity of the set of prime numbers There is a large body of work presenting important upper bounds on the complexity Supported in part by NSF grant CCR 9509603. y Supported in part by ARC grant A69700294. of the set of primes (including [AH87, APR83, Mil76, R80, SS77]) but as was pointed out recently in [BDS98a, BDS98b, BS99, Shp98] other than the work of [Med91] almost nothing has been published regarding lower bounds on the complexity of this set. It was not even known if primality testing could be accomplished by constant depth, polynomial size ....
M. Rabin. Probabilistic algorithm for primality testing, Journal of Number Theory, 12 (1980), 128--138.
The Rabin- Miller Probabilistic Primality Test: Some Results on.. - Higgins Self-citation (Rabin) (Correct)
....tests that can quickly determine if a given large number is prime with a certain confidence. One such test is the Rabin Miller probabilistic primality test. 2. Features of The Rabin Miller Probabilistic Primality Algorithm The Rabin Miller probabilistic primality test was developed by Rabin [3], based on Miller s [4] ideas. This algorithm provides a fast method of determining the primality of a number with a controllably small probability of error. The algorithm is described below. 2.1. The Rabin Miller Probabilistic Primality Algorithm Given (b,n) where n is the number to test for ....
....n is the number to test for primality, and b is randomly chosen in [1, n 1] Let n 1 = 2 q m, where m is an odd integer. If either (a) b m # 1 (mod n) or (b) there is an integer i in [0, q 1] such that b m2 i # 1 (mod n) then return inconclusive# else return n is composite. # Rabin [3], shows that the algorithm has the characteristic that for a composite number, n, at most 1 4 of the bases, b, will result in inconclusive.# The interpretation of the result inconclusive# is that so far the number n is acting as a prime (i.e. n may be prime) This characteristic is described ....
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Rabin, M.O., "Probabilistic Algorithm for Primality Testing" Journal of Number Theory. Vol. 12, 1980. pp. 128-138.
A Lower Bound for Primality - Eric Allender Dept (1999) (2 citations) (Correct)
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M. Rabin. Probabilistic algorithm for primality testing, Journal of Number Theory 12 (1980), 128--138.
Random Number Generation - L'Ecuyer (Correct)
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Rabin, M. O. (1980). Probabilistic algorithms for primality testing. J. Number Theory, Vol. 12, pp. 128--138.
About Polynomial-Time "unpredictable" Generators - L'Ecuyer, Proulx (Correct)
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Rabin, M. O. (1980). Probabilistic Algorithms for Primality Testing. J. Number Theory , 12, 128--138.
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