The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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ACM Computing Surveys (CSUR)
ACM Computing Surveys (CSUR)
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A method for obtaining digital signatures and public-key cryptosystems
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A linear sieve algorithm for finding prime numbers
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NP-complete decision problems for quadratic polynomials
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Relativized questions involving probabilistic algorithms
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Logics for probabilistic programming (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Tests for primality under the Riemann hypothesis
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The impact of complexity theory on algorithms for sparse polynomials
ACM SIGSAM Bulletin
Progress in computational complexity theory
Journal of Computer Science and Technology
Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi's RSA
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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ASID'09 Proceedings of the 3rd international conference on Anti-Counterfeiting, security, and identification in communication
Riemann's hypothesis and tests for primality
Journal of Computer and System Sciences
Deterministic polynomial time equivalence between factoring and key-recovery attack on Takagi's RSA
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Low-cost client puzzles based on modular exponentiation
ESORICS'10 Proceedings of the 15th European conference on Research in computer security
Emulating primality with multiset representations of natural numbers
ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
New online/offline signature schemes without random oracles
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Efficient modular exponentiation-based puzzles for denial-of-service protection
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
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The purpose of this paper is to present new upper bounds on the complexity of algorithms for testing the primality of a number. The first upper bound is 0(n&frac17;); it improves the previously best known bound of 0(n¼) due to Pollard [11]. The second upper bound is dependent on the Extended Riemann Hypothesis (ERH): assuming ERH, we produce an algorithm which tests primality and runs in time 0((log n)4) steps. Thus we show that primality is testable in time a polynomial in the length of the binary representation of a number. Finally, we give a partial solution to the relationship between the complexity of computing the prime factorization of a number, computing the Euler phi function, and computing other related functions.