Elliptic Curve research papers

  
Abstract

The abstract should be one paragraph of between 150 and  250 words. It is not indented. Section titles, such as the word Abstract  above, are not considered headings so they don’t use bold heading format.  Instead, use the Section Title style. This style automatically starts your  section on a new page, so you don’t have to add page breaks. (To see your  document with pagination, on the View tab, click Reading View.) Note that all  text styles for this template are available on the Home tab of the ribbon, in  the Styles gallery.
Keywords: Add  keywords here. To replace this (or any) tip text with your own, just select it  and then start typing. Don’t include space to  the right or left of the characters in your selection.
Add Title Here, up to 12 Words, on  One to Two Lines
The  body of your paper uses a half-inch first line indent and is double-spaced.  APA style provides for up to five heading levels, shown in the paragraphs that  follow. Note that the word Introduction should not be used as  an initial heading, as it’s assumed that your paper begins with an  introduction.
Literature Review
The first two heading levels  get their own paragraph, as shown here. Headings 3, 4, and 5 are run-in  headings used at the beginning of the paragraph.

Heading 21
For APA formatting requirements,  it’s easy to just type your own footnote references and notes. To format a  footnote reference, select the number and then, on the Home tab, in the Styles  gallery, click Footnote Reference.
Heading  3.
Include a period at the end of a  run-in heading. Note that you can include consecutive paragraphs with their  own headings, where appropriate. 
Heading 4.
When using headings, don’t skip  levels. If you need a heading 3, 4, or 5 with no text following it before the  next heading, just add a period at the end of the heading and then start a new  paragraph for the subheading and its text. (Last Name, Year)
Heading 5.
Like all sections of your  paper, references start on their own page, as you see on the page that  follows. Just type in-text citations as you do any text of your paper, as  shown at the end of this paragraph and the preceding paragraph. (Last Name, Year)
Discussion
The first two heading levels  get their own paragraph, as shown here. Headings 3, 4, and 5 are run-in  headings used at the beginning of the paragraph.

Heading 21
For APA formatting  requirements, it’s easy to just type your own footnote references and notes.  To format a footnote reference, select the number and then, on the Home tab,  in the Styles gallery, click Footnote Reference.
Heading  3.
Include a period at the end of a  run-in heading. Note that you can include consecutive paragraphs with their  own headings, where appropriate. 
Heading 4.
When using headings, don’t skip  levels. If you need a heading 3, 4, or 5 with no text following it before the  next heading, just add a period at the end of the heading and then start a new  paragraph for the subheading and its text. (Last Name, Year)
Heading 5.
Like all sections of your paper,  references start on their own page, as you see on the page that follows. Just  type in-text citations as you do any text of your paper, as shown at the end  of this paragraph and the preceding paragraph. (Last Name, Year)
  
Conclusion and Future Study
The first two heading levels  get their own paragraph, as shown here. Headings 3, 4, and 5 are run-in  headings used at the beginning of the paragraph.

Heading 21
For APA formatting  requirements, it’s easy to just type your own footnote references and notes.  To format a footnote reference, select the number and then, on the Home tab,  in the Styles gallery, click Footnote Reference.
Heading  3.
Include a period at the end of  a run-in heading. Note that you can include consecutive paragraphs with their  own headings, where appropriate. 
Heading 4.
When using headings, don’t skip  levels. If you need a heading 3, 4, or 5 with no text following it before the  next heading, just add a period at the end of the heading and then start a new  paragraph for the subheading and its text. (Last Name, Year)
Heading 5.
Like all sections of your paper,  references start on their own page, as you see on the page that follows. Just  type in-text citations as you do any text of your paper, as shown at the end  of this paragraph and the preceding paragraph. (Last Name, Year)

References

Last Name, F. M.    (Year). Article Title. Journal Title, Pages From – To.

Last Name, F. M.    (Year). Book Title. City Name: Publisher Name
Footnotes

1Add footnotes, if  any, on their own page following references. The body of a footnote, such as  this example, uses the Normal text style. (Note: If you delete this sample footnote,  don’t forget to delete its in-text reference as well. That’s at the end of the  sample Heading 2 paragraph on the first page of body content in this  template.)