关于OpenSSL命令RSA密钥生成（128位）

我使用的是OpenSSL版本1.0.2j

$ openssl version
OpenSSL 1.0.2j  26 Sep 2016

我生成一个32位密钥用于学习：

$ openssl genrsa -out key.pem 32; openssl rsa -in key.pem -text -noout
Generating RSA private key, 32 bit long modulus
.+++++++++++++++++++++++++++
.+++++++++++++++++++++++++++
e is 65537 (0x10001)
Private-Key: (32 bit)
modulus: 3049905109 (0xb5c9dbd5)
publicExponent: 65537 (0x10001)
privateExponent: 643259637 (0x26575cf5)
prime1: 59747 (0xe963)
prime2: 51047 (0xc767)
exponent1: 34201 (0x8599)
exponent2: 28991 (0x713f)
coefficient: 570 (0x23a)

我测试了59747*51047==3049905109，所以这是正确的

然后我尝试生成128位：

$ openssl genrsa -out key.pem 128; openssl rsa -in key.pem -text -noout
Generating RSA private key, 128 bit long modulus
.....+++++++++++++++++++++++++++
.+++++++++++++++++++++++++++
e is 65537 (0x10001)
Private-Key: (128 bit)
modulus:
    00:d7:f5:7b:f4:ac:b3:d6:ab:69:e9:f8:46:89:80:
    ad:a7
publicExponent: 65537 (0x10001)
privateExponent:
    00:96:69:0e:9d:5a:0f:a3:49:d5:f2:7f:5b:d5:bd:
    d5:71
prime1: 4077820879 (0xf30e9bcf)
prime2: 1063358121 (0x3f618ea9)
exponent1: 843651503 (0x324919af)
exponent2: 245467033 (0xea18799)
coefficient: 3957324193 (0xebdff9a1)

显然0xf30e9bcf*0x3f618ea9=3C2D385388980ADA7，但模数为00d7f57bf4acb3d6ab69e9f8468980ada7

---

看起来最后8个十六进制数字是正确的，但其他数字不一样。我不明白为什么会这样。有人能解释一下吗？

打印命令似乎有些混乱，它将

prime1

和

prime2

（和朋友）打印为32位值，而不是64位值

这是

F798F9F1F30E9BCF

*

DF49A5063F618EA9

OpenSSL命令打印每个基本因子的底部32位，而不是完整的64位

由于此乘法中没有mod，因此结果的底部32位与修剪后的值是正确的，这只是由于乘法。（回想一下用长格式写出两个长数字的乘法……现在用十六进制）

我多次运行该命令，它总是打印CRT值的64位值：

$ openssl genrsa 128 | openssl rsa -text
Generating RSA private key, 128 bit long modulus
.+++++++++++++++++++++++++++
...+++++++++++++++++++++++++++
e is 65537 (0x10001)
Private-Key: (128 bit)
modulus:
    00:e9:e2:0f:ed:54:89:0c:e7:4c:a0:c5:52:8f:c3:
    85:c3
publicExponent: 65537 (0x10001)
privateExponent:
    00:b5:bc:a8:dd:a5:3b:9d:9e:bd:80:57:b6:b2:ff:
    f3:d1
prime1: 17667776196693030377 (0xf5308cd7cefd75e9)
prime2: 17596097080145549003 (0xf431e510f75d16cb)
exponent1: 10532946027144870681 (0x922c8a9b1254fb19)
exponent2: 7661660226727396529 (0x6a53af620bd344b1)
coefficient: 1528899226626897395 (0x1537bdbf047735f3)
writing RSA key
-----BEGIN RSA PRIVATE KEY-----
MGMCAQACEQDp4g/tVIkM50ygxVKPw4XDAgMBAAECEQC1vKjdpTudnr2AV7ay//PR
AgkA9TCM1879dekCCQD0MeUQ910WywIJAJIsipsSVPsZAghqU69iC9NEsQIIFTe9
vwR3NfM=
-----END RSA PRIVATE KEY-----

进一步研究，问题似乎发生在64位系统上，

long

仍然是32位

:

由于我的

64位长

我的打印命令适用于33位到64位的范围

$ uname -srmo
Linux 4.4.0-119-generic x86_64 GNU/Linux

$ head -2 /etc/os-release
NAME="Ubuntu"
VERSION="16.04.4 LTS (Xenial Xerus)"

---

非常感谢您的回复！在Windows上，long似乎是32位。这就是为什么它只显示底部的32位。

$ grep SIXTY_FOUR `locate opensslconf.h | grep ^/usr`
#define SIXTY_FOUR_BIT_LONG
#undef SIXTY_FOUR_BIT

$ uname -srmo
Linux 4.4.0-119-generic x86_64 GNU/Linux

$ head -2 /etc/os-release
NAME="Ubuntu"
VERSION="16.04.4 LTS (Xenial Xerus)"