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Algorithmic Number Theory

Overview of attention for book
Cover of 'Algorithmic Number Theory'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Shimura curve computations
  3. Altmetric Badge
    Chapter 2 The Decision Diffie-Hellman problem
  4. Altmetric Badge
    Chapter 3 Parallel implementation of Schönhage's integer GCD algorithm
  5. Altmetric Badge
    Chapter 4 The complete analysis of the binary Euclidean algorithm
  6. Altmetric Badge
    Chapter 5 Cyclotomy primality proving — Recent developments
  7. Altmetric Badge
    Chapter 6 Primality proving using elliptic curves: An update
  8. Altmetric Badge
    Chapter 7 Bounding smooth integers (extended abstract)
  9. Altmetric Badge
    Chapter 8 Factorization of the numbers of the form m 3 + c 2 m 2 + c 1 m + c 0
  10. Altmetric Badge
    Chapter 9 Modelling the yield of number field sieve polynomials
  11. Altmetric Badge
    Chapter 10 A Montgomery-like square root for the Number Field Sieve
  12. Altmetric Badge
    Chapter 11 Robert Bennion's “hopping sieve”
  13. Altmetric Badge
    Chapter 12 Trading time for space in prime number sieves
  14. Altmetric Badge
    Chapter 13 Do sums of 4 biquadrates have a positive density?
  15. Altmetric Badge
    Chapter 14 New experimental results concerning the Goldbach conjecture
  16. Altmetric Badge
    Chapter 15 Dense admissible sets
  17. Altmetric Badge
    Chapter 16 An analytic approach to smooth polynomials over finite fields
  18. Altmetric Badge
    Chapter 17 Generating a product of three primes with an unknown factorization
  19. Altmetric Badge
    Chapter 18 On the performance of signature schemes based on elliptic curves
  20. Altmetric Badge
    Chapter 19 NTRU: A ring-based public key cryptosystem
  21. Altmetric Badge
    Chapter 20 Finding length-3 positive Cunningham chains and their cryptographic significance
  22. Altmetric Badge
    Chapter 21 Reducing ideal arithmetic to linear algebra problems
  23. Altmetric Badge
    Chapter 22 Evaluation of linear relations between vectors of a lattice in euclidean space
  24. Altmetric Badge
    Chapter 23 An efficient parallel block-reduction algorithm
  25. Altmetric Badge
    Chapter 24 Fast multiprecision evaluation of series of rational numbers
  26. Altmetric Badge
    Chapter 25 A problem concerning a character sum
  27. Altmetric Badge
    Chapter 26 Formal power series and their continued fraction expansion
  28. Altmetric Badge
    Chapter 27 Imprimitive octic fields with small discriminants
  29. Altmetric Badge
    Chapter 28 A table of totally complex number fields of small discriminants
  30. Altmetric Badge
    Chapter 29 Generating arithmetically equivalent number fields with elliptic curves
  31. Altmetric Badge
    Chapter 30 Computing the lead term of an abelian L-function
  32. Altmetric Badge
    Chapter 31 Timing analysis of targeted hunter searches
  33. Altmetric Badge
    Chapter 32 On successive minima of rings of algebraic integers
  34. Altmetric Badge
    Chapter 33 Computation of relative quadratic class groups
  35. Altmetric Badge
    Chapter 34 Generating class fields using Shimura reciprocity
  36. Altmetric Badge
    Chapter 35 Irregularity of prime numbers over real quadratic fields
  37. Altmetric Badge
    Chapter 36 Experimental results on class groups of real quadratic fields
  38. Altmetric Badge
    Chapter 37 Computation of relative class numbers of imaginary cyclic fields of 2-power degrees
  39. Altmetric Badge
    Chapter 38 Formal groups, elliptic curves, and some theorems of Couveignes
  40. Altmetric Badge
    Chapter 39 A comparison of direct and indirect methods for computing Selmer groups of an elliptic curve
  41. Altmetric Badge
    Chapter 40 An algorithm for approximate counting of points on algebraic sets over finite fields
  42. Altmetric Badge
    Chapter 41 S-integral points on elliptic curves and Fermat's triple equations
  43. Altmetric Badge
    Chapter 42 Speeding up Pollard's rho method for computing discrete logarithms
  44. Altmetric Badge
    Chapter 43 A general method of constructing global function fields with many rational places
  45. Altmetric Badge
    Chapter 44 Lattice basis reduction in function fields
  46. Altmetric Badge
    Chapter 45 Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic curves
  47. Altmetric Badge
    Chapter 46 Unit computation in purely cubic function fields of unit rank 1
  48. Altmetric Badge
    Chapter 47 An improved method of computing the regulator of a real quadratic function field
  49. Altmetric Badge
    Chapter 48 The equivalence between elliptic curve and quadratic function field discrete logarithms in characteristic 2
Attention for Chapter 19: NTRU: A ring-based public key cryptosystem
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About this Attention Score

  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (91st percentile)
  • High Attention Score compared to outputs of the same age and source (90th percentile)

Mentioned by

twitter
7 X users
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1 patent
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1 Facebook page
wikipedia
4 Wikipedia pages

Citations

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13 Dimensions

Readers on

mendeley
265 Mendeley
citeulike
1 CiteULike
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Chapter title
NTRU: A ring-based public key cryptosystem
Chapter number 19
Book title
Algorithmic Number Theory
Published in
Lecture notes in computer science, May 2006
DOI 10.1007/bfb0054868
Book ISBNs
978-3-54-064657-0, 978-3-54-069113-6
Authors

Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman, Hoffstein, Jeffrey, Pipher, Jill, Silverman, Joseph H.

X Demographics

X Demographics

The data shown below were collected from the profiles of 7 X users who shared this research output. Click here to find out more about how the information was compiled.
Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 265 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Japan 2 <1%
United States 2 <1%
Brazil 1 <1%
Unknown 260 98%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 51 19%
Student > Master 45 17%
Student > Bachelor 26 10%
Researcher 23 9%
Other 10 4%
Other 40 15%
Unknown 70 26%
Readers by discipline Count As %
Computer Science 116 44%
Mathematics 29 11%
Engineering 29 11%
Physics and Astronomy 6 2%
Materials Science 3 1%
Other 4 2%
Unknown 78 29%
Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 11. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 07 February 2024.
All research outputs
#3,430,990
of 25,998,826 outputs
Outputs from Lecture notes in computer science
#661
of 8,225 outputs
Outputs of similar age
#8,087
of 89,565 outputs
Outputs of similar age from Lecture notes in computer science
#4
of 42 outputs
Altmetric has tracked 25,998,826 research outputs across all sources so far. Compared to these this one has done well and is in the 86th percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 8,225 research outputs from this source. They typically receive a little more attention than average, with a mean Attention Score of 5.3. This one has done particularly well, scoring higher than 92% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 89,565 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 91% of its contemporaries.
We're also able to compare this research output to 42 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 90% of its contemporaries.