标题: 用指定数据(p、q、e)生成PEM文件

https://scz.617.cn/misc/201604271353.txt

openssl的genrsa不能任意指定e，只有3和65537两种选择。numbits必须不小于32。

帮助里所谓的F4是指第4个(从0计)费马素数:

F0=2^(2^0)+1=3
F1=2^(2^1)+1=5
F2=2^(2^2)+1=17
F3=2^(2^3)+1=257
F4=2^(2^4)+1=65537

openssl的genpkey可以任意指定e。numbits必须不小于256。

有时你想用指定数据生成PEM文件，而不是让openssl替你生成p、q。比如你想用这组
数据:

--------------------------------------------------------------------------
p=17
q=19
n=p*q=323
φ(n)=(p-1)*(q-1)=288
e=11
d=e^(-1)(mod φ(n))=131
d mod (p-1)=3
d mod (q-1)=5
(inverse of q) mod p=9
--------------------------------------------------------------------------

如果写C程序，没什么好说的。下面介绍一种奇技淫巧，只靠openssl命令达成目标。

$ vi privatekey.conf

--------------------------------------------------------------------------
asn1=SEQUENCE:any

[any]
version=INTEGER:0
n=INTEGER:323
e=INTEGER:11
d=INTEGER:131
p=INTEGER:17
q=INTEGER:19
d_mod_p_1=INTEGER:3
d_mod_q_1=INTEGER:5
inverse_q_p=INTEGER:9
--------------------------------------------------------------------------

$ openssl asn1parse -genconf privatekey.conf -out privatekey.der
    0:d=0  hl=2 l=  29 cons: SEQUENCE
    2:d=1  hl=2 l=   1 prim: INTEGER           :00
    5:d=1  hl=2 l=   2 prim: INTEGER           :0143
    9:d=1  hl=2 l=   1 prim: INTEGER           :0B
   12:d=1  hl=2 l=   2 prim: INTEGER           :83
   16:d=1  hl=2 l=   1 prim: INTEGER           :11
   19:d=1  hl=2 l=   1 prim: INTEGER           :13
   22:d=1  hl=2 l=   1 prim: INTEGER           :03
   25:d=1  hl=2 l=   1 prim: INTEGER           :05
   28:d=1  hl=2 l=   1 prim: INTEGER           :09
$ openssl rsa -in privatekey.der -inform DER -text -noout -check
Private-Key: (9 bit)
modulus: 323 (0x143)
publicExponent: 11 (0xb)
privateExponent: 131 (0x83)
prime1: 17 (0x11)
prime2: 19 (0x13)
exponent1: 3 (0x3)
exponent2: 5 (0x5)
coefficient: 9 (0x9)
RSA key ok
$ openssl rsa -in privatekey.der -inform DER -out privatekey.pem -outform PEM

$ openssl asn1parse -i -dump -in privatekey.pem
    0:d=0  hl=2 l=  29 cons: SEQUENCE
    2:d=1  hl=2 l=   1 prim:  INTEGER           :00
    5:d=1  hl=2 l=   2 prim:  INTEGER           :0143
    9:d=1  hl=2 l=   1 prim:  INTEGER           :0B
   12:d=1  hl=2 l=   2 prim:  INTEGER           :83
   16:d=1  hl=2 l=   1 prim:  INTEGER           :11
   19:d=1  hl=2 l=   1 prim:  INTEGER           :13
   22:d=1  hl=2 l=   1 prim:  INTEGER           :03
   25:d=1  hl=2 l=   1 prim:  INTEGER           :05
   28:d=1  hl=2 l=   1 prim:  INTEGER           :09
$ openssl rsa -in privatekey.pem -inform PEM -text -noout -check
Private-Key: (9 bit)
modulus: 323 (0x143)
publicExponent: 11 (0xb)
privateExponent: 131 (0x83)
prime1: 17 (0x11)
prime2: 19 (0x13)
exponent1: 3 (0x3)
exponent2: 5 (0x5)
coefficient: 9 (0x9)
RSA key ok

$ cat privatekey.pem
-----BEGIN RSA PRIVATE KEY-----
MB0CAQACAgFDAgELAgIAgwIBEQIBEwIBAwIBBQIBCQ==
-----END RSA PRIVATE KEY-----

$ openssl rsa -pubout -in privatekey.pem -out publickey.pem
$ openssl asn1parse -i -dump -in publickey.pem
$ openssl asn1parse -i -dump -strparse 17 -in publickey.pem
    0:d=0  hl=2 l=   7 cons: SEQUENCE
    2:d=1  hl=2 l=   2 prim:  INTEGER           :0143
    6:d=1  hl=2 l=   1 prim:  INTEGER           :0B
$ openssl rsa -pubin -in publickey.pem -inform PEM -text -noout
Public-Key: (9 bit)
Modulus: 323 (0x143)
Exponent: 11 (0xb)

$ cat publickey.pem
-----BEGIN PUBLIC KEY-----
MBswDQYJKoZIhvcNAQEBBQADCgAwBwICAUMCAQs=
-----END PUBLIC KEY-----

别问我为什么有这个需求，你又不是上帝。