Primality testing revisited

@inproceedings{Davenport1992PrimalityTR,
  title={Primality testing revisited},
  author={James H. Davenport},
  booktitle={International Symposium on Symbolic and Algebraic Computation},
  year={1992}
}
  • J. Davenport
  • Published in
    International Symposium on…
     1 August 1992
  • Mathematics
Rabin’s algorithm is commonly used in computer algebra systems and elsewhere for primality testing. This paper presents an experience with this in the Axiom* computer algebra system. As a result of this experience, we suggest certain strengthenings of the algorithm. 
View on ACM
staff.bath.ac.uk
11 Citations
Highly Influential Citations
1
Background Citations
3

11 Citations

Some Primality Testing Algorithms

  • R. Pinch
  • Computer Science, Mathematics
  • 1993
We describe the primality testing algorithms in use in some popular computer algebra systems, and give some examples where they break down in practice.

Efficient polynomial time algorithms computing industrial-strength primitive roots

The Carmichael Numbers up to 10 15

We extend our previous computations to show that there are 1401644 Carmichael numbers up to 10 18 . As before, the numbers were generated by a back-tracking search for possible prime factorisations…

A Bias-Free Quantum Random Number Generation Using Photon Arrival Time Selectively

We present a high-quality bias-free quantum random number generator (QRNG) using photon arrival time selectively, in accordance with the number of photon detection events within a sampling time…

Design Trade Studies , and Risk and Uncertainty in Collaborative Design and Model Based Engineering : Methods , Tools , Research , and Practice

Complex systems engineering projects are increasingly prevalent in our world. Technical requirements for complex systems usually break out individual subsystems parameters. For instance, each…

Cited References

A Study on Decision Making Procedures for Reduction of Carbon Emission and Energy Consumption of Process Systems

A Study on Decision Making Procedures for Reduction of Carbon Emission and Energy Consumption of Process Systems Seunghyok Kim School of Chemical and Biological Engineering The graduate school Seoul…

Robust efficient distributed RSA-key generation

The disclosed method can be combined with proactive function sharing techniques to establish the first efficient, optimal-resilience, robust and proactively-secure RSA-based distributed trust services where the key is never entrusted to a single entity.

Primality testing of large numbers in Maple

  • S. Yan
  • Mathematics, Computer Science
  • 1995

Pseudoprimes: A Survey of Recent Results

Public key cryptosystems require the use of large prime numbers, numbers with at least 256 bits (80 decimal digits), and one way of dealing with this problem is to use special primes built up using the converse of Fermat's theorem.

References

SHOWING 1-10 OF 26 REFERENCES

Probabilistic algorithm for testing primality

Distributed Primality Proving and the Primality of (23539+1)/3

  • F. Morain
  • Mathematics, Computer Science
    EUROCRYPT
  • 1990
The successful attempt at proving the primality of the l065-digit (23539+1)/3, the first ordinary Titanic prime, is described.

Explicit bounds for primality testing and related problems

Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits…

Analytic methods in the analysis and design of number-theoretic algorithms

  • E. Bach
  • Computer Science, Mathematics
  • 1985
This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic…

On strong pseudoprimes to several bases

With Y'k denoting the smallest strong pseudoprime to all of the first k primes taken as bases we determine the exact values for 5, q6, q7, q8 and give upper bounds for V/9, / W t,' 1 . We discuss the…

A Course in Number Theory and Cryptography

Statistical evidence for small generating sets

This work gives additional evidence, independent of the ERH, that primality testing can be done in deterministic polynomial time; if the bound on G(n) is correct, there is a deterministic primality test using O(log n)2 multiplications modulo n.

Private communication

vii

Modifications 18459366157::I, 21276028621::I ]::(List I) O(log4N) Modifications

  • 1980

Pinch 1993] and Jaeschke 1993] Modiications The following global declarations are made

  • Pinch 1993] and Jaeschke 1993] Modiications The following global declarations are made
  • 1980