tinyec

tinyec

Perpustakaan kecil untuk melakukan operasi aritmatika pada kurva elips dengan python murni. Tidak ada ketergantungan.

Ini bukan perpustakaan yang cocok untuk produksi. Hal ini berguna bagi para profesional keamanan untuk memahami cara kerja EC, dan dapat bermain dengan kurva yang telah ditentukan sebelumnya.

instalasi

pip install tinyec

penggunaan

Ada 2 kelas utama:

• Curve(), yang menggambarkan kurva elips dalam bidang berhingga
• Point(), yang menggambarkan suatu titik milik EC

Peringatan Perhitungan pada titik di luar kurva diperbolehkan. Mereka hanya akan memberikan peringatan.

mengerjakan kurva yang ada

Contoh penggunaan pada sampel rutin NIST => https://www.nsa.gov/ia/_files/nist-routines.pdf:

 >> > import tinyec . ec as ec
>> > import tinyec . registry as reg
>> > c = reg . get_curve ( "secp192r1" )
>> > s = ec . Point ( c , 0xd458e7d127ae671b0c330266d246769353a012073e97acf8 , 0x325930500d851f336bddc050cf7fb11b5673a1645086df3b )
>> > t = ec . Point ( c , 0xf22c4395213e9ebe67ddecdd87fdbd01be16fb059b9753a4 , 0x264424096af2b3597796db48f8dfb41fa9cecc97691a9c79 )
>> > r = s + t
>> > r
( 1787070900316344022479363585363935252075532448940096815760 , 1583034776780933252095415958625802984888372377603917916747 ) on secp192r1 = > y ^ 2 = x ^ 3 + 6277101735386680763835789423207666416083908700390324961276 x + 2455155546008943817740293915197451784769108058161191238065 
( mod 6277101735386680763835789423207666416083908700390324961279 )
>> > hex ( r . x )
'0x48e1e4096b9b8e5ca9d0f1f077b8abf58e843894de4d0290L'
>> > hex ( r . y )
'0x408fa77c797cd7dbfb16aa48a3648d3d63c94117d7b6aa4bL'
>> > r = s - t
>> > r
( 6193438478050209507979672067809269724375390027440522152494 , 226636415264149817017346905052752138772359775362461041003 ) on secp192r1 = > y ^ 2 = x ^ 3 + 6277101735386680763835789423207666416083908700390324961276 x + 2455155546008943817740293915197451784769108058161191238065 (
mod 6277101735386680763835789423207666416083908700390324961279 )
>> > hex ( r . x )
'0xfc9683cc5abfb4fe0cc8cc3bc9f61eabc4688f11e9f64a2eL'
>> > hex ( r . y )
'0x93e31d00fb78269732b1bd2a73c23cdd31745d0523d816bL'
>> > r = 2 * s
>> > r
( 1195895923065450997501505402941681398272052708885411031394 , 340030206158745947396451508065335698335058477174385838543 ) on secp192r1 = > y ^ 2 = x ^ 3 + 6277101735386680763835789423207666416083908700390324961276 x + 2455155546008943817740293915197451784769108058161191238065 (
mod 6277101735386680763835789423207666416083908700390324961279 )
>> > hex ( r . x )
'0x30c5bc6b8c7da25354b373dc14dd8a0eba42d25a3f6e6962L'
>> > hex ( r . y )
'0xdde14bc4249a721c407aedbf011e2ddbbcb2968c9d889cfL'
>> > d = 0xa78a236d60baec0c5dd41b33a542463a8255391af64c74ee
>> > r = d * s
>> > hex ( r . x )
'0x1faee4205a4f669d2d0a8f25e3bcec9a62a6952965bf6d31L'
>> > hex ( r . y )
'0x5ff2cdfa508a2581892367087c696f179e7a4d7e8260fb06L'
>> > e = 0xc4be3d53ec3089e71e4de8ceab7cce889bc393cd85b972bc
>> > r = d * s + e * t
>> > r
( 39786866609245082371772779541859439402855864496422607838 , 547967566579883709478937502153554894699060378424501614148 ) on secp192r1 = > y ^ 2 = x ^ 3 + 6277101735386680763835789423207666416083908700390324961276 x + 2455155546008943817740293915197451784769108058161191238065 ( mo
d 6277101735386680763835789423207666416083908700390324961279 )
>> > hex ( r . x )
'0x19f64eed8fa9b72b7dfea82c17c9bfa60ecb9e1778b5bdeL'
>> > hex ( r . y )
'0x16590c5fcd8655fa4ced33fb800e2a7e3c61f35d83503644L'

mengerjakan kurva khusus

Jika perlu, Anda juga dapat mengerjakan lekuk tubuh Anda sendiri. Di sini kita ambil medan prima 97, dengan titik generator (1, 2), orde 5 dan kofaktor 1:

 >> > import tinyec . ec as ec
>> > field = ec . SubGroup ( 97 , ( 1 , 2 ), 5 , 1 )
>> > curve = ec . Curve ( 2 , 3 , field )
tinyec / ec . py : 115 : UserWarning : Point ( 1 , 2 ) is not on curve "undefined" = > y ^ 2 = x ^ 3 + 2 x + 3 ( mod 97 )
  warnings . warn ( "Point (%d, %d) is not on curve %s" % ( self . x , self . y , self . curve ))
>> > # Warning is generated because the generator point does not belong to the curve
>> > p1 = ec . Point ( curve , - 5 , 3 )
>> > p1 . on_curve
False
>> > p2 = ec . Point ( curve , 22 , 5 )
>> > p2 . on_curve
True
>> > print ( p1 + p2 )
( 18 , 42 ) off "undefined" = > y ^ 2 = x ^ 3 + 2 x + 3 ( mod 97 )