我怎样才能得到椭圆曲线的点？

Question

我已经设置了与facebook.com的连接，我需要签名中使用的点。我有公钥和证书。也是通过以下命令：

openssl ec -pubin -in facebook_pub.key -noout -text -param_enc explicit

我得到了输出：

read EC key
Public-Key: (256 bit)
pub:
    04:a0:f1:8c:af:a7:39:88:68:5b:13:56:0e:15:15:
    b4:a7:45:ef:1b:c7:e5:85:3c:2b:04:d4:65:8a:31:
    31:22:ea:a3:92:ed:64:9d:ba:65:81:e3:b6:12:76:
    d8:b3:0b:45:f1:ff:0a:28:14:9c:4f:dc:73:a9:b3:
    49:2d:a0:76:d3
Field Type: prime-field
Prime:
    00:ff:ff:ff:ff:00:00:00:01:00:00:00:00:00:00:
    00:00:00:00:00:00:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:ff:ff
A:   
    00:ff:ff:ff:ff:00:00:00:01:00:00:00:00:00:00:
    00:00:00:00:00:00:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:ff:fc
B:   
    5a:c6:35:d8:aa:3a:93:e7:b3:eb:bd:55:76:98:86:
    bc:65:1d:06:b0:cc:53:b0:f6:3b:ce:3c:3e:27:d2:
    60:4b
Generator (uncompressed):
    04:6b:17:d1:f2:e1:2c:42:47:f8:bc:e6:e5:63:a4:
    40:f2:77:03:7d:81:2d:eb:33:a0:f4:a1:39:45:d8:
    98:c2:96:4f:e3:42:e2:fe:1a:7f:9b:8e:e7:eb:4a:
    7c:0f:9e:16:2b:ce:33:57:6b:31:5e:ce:cb:b6:40:
    68:37:bf:51:f5
Order: 
    00:ff:ff:ff:ff:00:00:00:00:ff:ff:ff:ff:ff:ff:
    ff:ff:bc:e6:fa:ad:a7:17:9e:84:f3:b9:ca:c2:fc:
    63:25:51
Cofactor:  1 (0x1)
Seed:
    c4:9d:36:08:86:e7:04:93:6a:66:78:e1:13:9d:26:
    b7:81:9f:7e:90

有了这个输出，我可以看到素数A，B和发生器。但我能看到Px和Py。有人知道我怎么能找到它吗？

Answer 1

这里有一种非常不雅致的方法来获取坐标。

根据RFC 5480节2.2，ECPoint的定义在SEC1 (第2.3.4条)中。

这一节的实质是：

• 删除0x04标记字节
• 取剩余字节
• 左半设为X
• 右半边和Y。

我在下面的坚牢 Python模块中完成了这一工作。

###Grab X组件忽略第一个字节。(只是一个标记值。)

$ openssl ec -pubin -in facebook_pub.key -noout -text -conv_form compressed 2>/dev/null | grep '^    ' | sed 's/://g' | xargs echo | sed 's/ //g'
03a0f18cafa73988685b13560e1515b4a745ef1bc7e5853c2b04d4658a313122ea

###Grab Y组件("Y“必须是"X”组件之后的字符串的其余部分。即在“22 e.”部分之后)

$ openssl ec -pubin -in facebook_pub.key -noout -text 2>/dev/null | grep '^    ' | sed 's/://g' | xargs echo | sed 's/ //g'

04a0f18cafa73988685b13560e1515b4a745ef1bc7e5853c2b04d4658a313122eaa392ed649dba6581e3b61276d8b30b45f1ff0a28149c4fdc73a9b3492da076d3

###Install“Collecting”python包$ time pip安装快速安装收集快件下载快捷键-1.6.1.tar.gz收集包的建筑车轮:运行setup.py bdist_wheel的快捷包。完成存储在目录中: /home/User/.cache/pip/wheels/93/8a/d3/be7fc222c030383ac6313be85c602762daafc2cac8fd547e44成功地构建了Successfully，安装了收集的软件包: Successfully成功地安装了Successfully 1.6.1

real    0m19.002s
user    0m4.909s
sys     0m4.102s

ipython内部的###Use $ ipython

In [1]: from fastecdsa.point import Point

In [2]: from fastecdsa.point import P256

In [3]: x=0xa0f18cafa73988685b13560e1515b4a745ef1bc7e5853c2b04d4658a313122ea

In [4]: y=0xa392ed649dba6581e3b61276d8b30b45f1ff0a28149c4fdc73a9b3492da076d3

In [5]: Point(1,2, curve=P256)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
 in ()
----> 1 Point(1,2, curve=P256)

/usr/lib/python2.7/site-packages/fastecdsa/point.pyc in __init__(self, x, y, curve)
     12     def __init__(self, x, y, curve=P256):
     13         if not curve.is_point_on_curve((x, y)):
---> 14             raise ValueError('(x, y) coordinates are not on curve <{}>'.format(curve.name))
     15         else:
     16             self.x = x

ValueError: (x, y) coordinates are not on curve 

In [6]: p=Point(x, y, curve=P256)

In [7]: p.x
Out[7]: 72796836896024250540670287871159592541946330786250779466423542213376197337834L

In [8]: p.y
Out[8]: 73986592417019630365603572314878953642162012803095695018690968405918923912915L

In [9]: p.curve
Out[9]: 

正如您在上面看到的:如果您向“Point(.)”提供无效的参数(如"1，2，curve=P256")，那么fastecdsa将引发错误。构造函数。