NIST Binary Curves Parameters
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The parameter sets of the five random binary elliptic curves standardized by NIST are listed below. The curves are of the form y^2 + xy = x^3 + x^2 + b over a binary field. For the five curves the following parameters are listed:
- p(t): the reduction polynomial (in explicit and hexadecimal form)
- b: the curve's b coefficient
- G_x, G_y: the x and y coordinates of the base point G
- n: the base point's order
- h: the curve's cofactor
Contents |
[edit]
B163
p(t) = t^163 + t^7 + t^6 + t^3 + 1
= 800000000000000000000000000000000000000C9
b = 20a601907b8c953ca1481eb10512f78744a3205fd
G_x = 3f0eba16286a2d57ea0991168d4994637e8343e36
G_y = 0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1
n = 5846006549323611672814742442876390689256843201587
h = 2
[edit]
B233
p(t) = t^233 + t^74 + 1
= 20000000000000000000000000000000000000004000000000000000001
b = 066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
G_x = 0fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
G_y = 1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
n = 6901746346790563787434755862277025555839812737345013555379383634485463
h = 2
[edit]
B283
p(t) = t^283 + t^12 + t^7 + t^5 + 1
= 800000000000000000000000000000000000000000000000000000000000000000010A1
b = 27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
G_x = 5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053
G_y = 3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4
n = 7770675568902916283677847627294075626569625924376904889109196526770044277787378692871
h = 2
[edit]
B409
p(t) = t^409 + t^87 + 1
= 2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
b = 021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
G_x = 15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7
G_y = 061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706
n = 661055968790248598951915308032771039828404682964281219284648798304157774827374805208143723762179110965979867288366567526771
h = 2
[edit]
B571
p(t) = t^571 + t^10 + t^5 + t^2 + 1
= 80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
b = 2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a
G_x = 303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19
G_y = 37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b
n = 3864537523017258344695351890931987344298927329706434998657235251451519142289560424536143999389415773083133881121926944486246872462816813070234528288303332411393191105285703
h = 2