NIST Koblitz Curves Parameters

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FIPS 186-2  (2000) 
National Institute of Standards and Technology
from the Federal Information Processing Standards (FIPS) Publication Series of the National Institute of Standards and Technology (NIST)

The parameter sets of the five binary koblitz curves standardized by NIST are listed below. The curves are of the form y^2 + xy = x^3 + ax^2 + 1 over a binary field. For the five curves the following parameters are listed:

  1. p(t): the reduction polynomial (in explicit and hexadecimal form)
  2. a: the curve's a coefficient
  3. G_x, G_y: the x and y coordinates of the base point G
  4. n: the base point's order
  5. h: the curve's cofactor

K163[edit]

p(t) = t^163 + t^7 + t^6 + t^3 + 1 
     = 800000000000000000000000000000000000000C9
a    = 1
G_x  = 2fe13c0537bbc11acaa07d793de4e6d5e5c94eee8
G_y  = 289070fb05d38ff58321f2e800536d538ccdaa3d9
n    = 5846006549323611672814741753598448348329118574063
h    = 2

K233[edit]

p(t) = t^233 + t^74 + 1
     = 20000000000000000000000000000000000000004000000000000000001
a    = 0
G_x  = 17232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126
G_y  = 1db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3
n    = 3450873173395281893717377931138512760570940988862252126328087024741343
h    = 4

K283[edit]

p(t) = t^283 + t^12 + t^7 + t^5 + 1
     = 800000000000000000000000000000000000000000000000000000000000000000010A1
a    = 0
G_x  = 503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836
G_y  = 1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259
n    = 3885337784451458141838923813647037813284811733793061324295874997529815829704422603873
h    = 4

K409[edit]

p(t) = t^409 + t^87 + 1
     = 2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
a    = 0
G_x  = 060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746
G_y  = 1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b
n    = 330527984395124299475957654016385519914202341482140609642324395022880711289249191050673258457777458014096366590617731358671
h    = 4

K571[edit]

p(t) = t^571 + t^10 + t^5 + t^2 + 1
     = 80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
a    = 0
G_x  = 26eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972
G_y  = 349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3
n    = 1932268761508629172347675945465993672149463664853217499328617625725759571144780212268133978522706711834706712800825351461273674974066617311929682421617092503555733685276673
h    = 4


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