@MISC{PEPIN.MIZ,
  AUTHOR = {Fujisawa, Yoshinori and Fuwa, Yasushi and Shimizu, Hidetaka},
  TITLE = {Public-Key Cryptography and {P}epin's Test for the Primality of {F}ermat Numbers},
  SECTION1 = {Some Useful Theorems},
  SECTION2 = {Public-Key Cryptography},
  SECTION3 = {Order's Function},
  SECTION4 = {Fermat Number},
  SECTION5 = {Pepin's Test},
  DAY = {21},
  MONTH = {December},
  YEAR = {1998},
  ADDRESS1 = {Shinshu University\\Nagano},
  ADDRESS2 = {Shinshu University\\Nagano},
  ADDRESS3 = {Information Technology Research Institute
of Nagano Prefecture},
  SUMMARY = {In this article, we have proved the correctness of the Public-Key
Cryptography and the Pepin's Test for the Primality of Fermat Numbers
 ($F(n) = 2^{2^n}+1$).
It is a very important result in the IDEA Cryptography that
F(4) is a prime number.
At first, we prepared some useful theorems. Then, we proved
the correctness of the Public-Key Cryptography. Next, we defined
the Order's function and proved some properties.
This function is very important in the proof of the Pepin's Test.
Next, we proved some theorems about the Fermat Number.
And finally, we proved the Pepin's Test using some properties of
the Order's Function. And using the obtained result we have proved
that F(1), F(2), F(3)
and F(4) are prime number.}}


@BOOK{prime,
       AUTHOR = {Paulo Ribenboim},
        TITLE = {The World of Prime Numbers},
    PUBLISHER = {Kyoritsu Publishing Co., Ltd.},
         YEAR = {1995},
      EDITION = {Second}}