On Linux, using the following command generated this key:
openssl genrsa -out rsa_1024_priv.pem 1024
To understand how the key is broken down into its respective
components, execute the following additional command:
openssl rsa -text -in rsa_1024_priv.pem
Alternatively, you can do what I did and breakdown the individual
components by hand - in order to learn how the data structure
actually works.
Firstly, the data block has to be decoded from it's standard
Base64 format, so remove the "-----BEGIN..." lines at the start
and end of the file and convert the data into Hexadecimal.
The data block is now in a format we can read (sort of).
Using Abstract Syntax Notation 1 (or ASN.1), we can read and
identify the Distinguished Encoding Rules (DER) encoded components
contained within this data.
Although the only data stored in this instance of the ASN format
is of type Integer, other standard variable types are listed here
for clarity. When the Integer type is used in this context, it is
followed by the length in bytes for the following data object, and
then the data itself, as can be seen below.
-----BEGIN RSA PRIVATE KEY----- MIICXgIBAAKBgQDHikastc8+I81zCg/qWW8dMr8mqvXQ3qbPAmu0RjxoZVI47tvs kYlFAXOf0sPrhO2nUuooJngnHV0639iTTEYG1vckNaW2R6U5QTdQ5Rq5u+uV3pMk 7w7Vs4n3urQ6jnqt2rTXbC1DNa/PFeAZatbf7ffBBy0IGO0zc128IshYcwIDAQAB AoGBALTNl2JxTvq4SDW/3VH0fZkQXWH1MM10oeMbB2qO5beWb11FGaOO77nGKfWc bYgfp5Ogrql4yhBvLAXnxH8bcqqwORtFhlyV68U1y4R+8WxDNh0aevxH8hRS/1X5 031DJm1JlU0E+vStiktN0tC3ebH5hE+1OxbIHSZ+WOWLYX7JAkEA5uigRgKp8ScG auUijvdOLZIhHWq7y5Wz+nOHUuDw8P7wOTKU34QJAoWEe771p9Pf/GTA/kr0BQnP QvWUDxGzJwJBAN05C6krwPeryFKrKtjOGJIniIoY72wRnoNcdEEs3HDRhf48YWFo riRbZylzzzNFy/gmzT6XJQTfktGqq+FZD9UCQGIJaGrxHJgfmpDuAhMzGsUsYtTr iRox0D1Iqa7dhE693t5aBG010OF6MLqdZA1CXrn5SRtuVVaCSLZEL/2J5UcCQQDA d3MXucNnN4NPuS/L9HMYJWD7lPoosaORcgyK77bSSNgk+u9WSjbH1uYIAIPSffUZ bti+jc1dUg5wb+aeZlgJAkEAurrpmpqj5vg087ZngKfFGR5rozDiTsK5DceTV97K a3Y+Nzl+XWTxDBWk4YPh2ZlKv402hZEfWBYxUDn5ZkH/bw== -----END RSA PRIVATE KEY-----
In this example, the Hexadecimal values have been paired for clarity,
but in the other examples (see links at the top of this page) the
values have not been separated.
Parts highlighted below, in order:
-----BEGIN RSA PRIVATE KEY-----
30 82 02 5e 02 01 00 02 81 81 00 c7 8a 46 ac b5 cf 3e 23 cd 73 0a
0f ea 59 6f 1d 32 bf 26 aa f5 d0 de a6 cf 02 6b b4 46 3c 68 65 52
38 ee db ec 91 89 45 01 73 9f d2 c3 eb 84 ed a7 52 ea 28 26 78 27
1d 5d 3a df d8 93 4c 46 06 d6 f7 24 35 a5 b6 47 a5 39 41 37 50 e5
1a b9 bb eb 95 de 93 24 ef 0e d5 b3 89 f7 ba b4 3a 8e 7a ad da b4
d7 6c 2d 43 35 af cf 15 e0 19 6a d6 df ed f7 c1 07 2d 08 18 ed 33
73 5d bc 22 c8 58 73 02 03 01 00 01 02 81 81 00 b4 cd 97 62 71 4e
fa b8 48 35 bf dd 51 f4 7d 99 10 5d 61 f5 30 cd 74 a1 e3 1b 07 6a
8e e5 b7 96 6f 5d 45 19 a3 8e ef b9 c6 29 f5 9c 6d 88 1f a7 93 a0
ae a9 78 ca 10 6f 2c 05 e7 c4 7f 1b 72 aa b0 39 1b 45 86 5c 95 eb
c5 35 cb 84 7e f1 6c 43 36 1d 1a 7a fc 47 f2 14 52 ff 55 f9 d3 7d
43 26 6d 49 95 4d 04 fa f4 ad 8a 4b 4d d2 d0 b7 79 b1 f9 84 4f b5
3b 16 c8 1d 26 7e 58 e5 8b 61 7e c9 02 41 00 e6 e8 a0 46 02 a9 f1
27 06 6a e5 22 8e f7 4e 2d 92 21 1d 6a bb cb 95 b3 fa 73 87 52 e0
f0 f0 fe f0 39 32 94 df 84 09 02 85 84 7b be f5 a7 d3 df fc 64 c0
fe 4a f4 05 09 cf 42 f5 94 0f 11 b3 27 02 41 00 dd 39 0b a9 2b c0
f7 ab c8 52 ab 2a d8 ce 18 92 27 88 8a 18 ef 6c 11 9e 83 5c 74 41
2c dc 70 d1 85 fe 3c 61 61 68 ae 24 5b 67 29 73 cf 33 45 cb f8 26
cd 3e 97 25 04 df 92 d1 aa ab e1 59 0f d5 02 40 62 09 68 6a f1 1c
98 1f 9a 90 ee 02 13 33 1a c5 2c 62 d4 eb 89 1a 31 d0 3d 48 a9 ae
dd 84 4e bd de de 5a 04 6d 35 d0 e1 7a 30 ba 9d 64 0d 42 5e b9 f9
49 1b 6e 55 56 82 48 b6 44 2f fd 89 e5 47 02 41 00 c0 77 73 17 b9
c3 67 37 83 4f b9 2f cb f4 73 18 25 60 fb 94 fa 28 b1 a3 91 72 0c
8a ef b6 d2 48 d8 24 fa ef 56 4a 36 c7 d6 e6 08 00 83 d2 7d f5 19
6e d8 be 8d cd 5d 52 0e 70 6f e6 9e 66 58 09 02 41 00 ba ba e9 9a
9a a3 e6 f8 34 f3 b6 67 80 a7 c5 19 1e 6b a3 30 e2 4e c2 b9 0d c7
93 57 de ca 6b 76 3e 37 39 7e 5d 64 f1 0c 15 a4 e1 83 e1 d9 99 4a
bf 8d 36 85 91 1f 58 16 31 50 39 f9 66 41 ff 6f
-----END RSA PRIVATE KEY-----
Private-Key:
header:
30 82 02 5e (0x3082 == ASN.1 Sequence)
separator:
02 01 (0x02 == Integer and 0x01 == 1 byte long)
algorithm version:
00 (0x00 == version zero)
separator:
02 81 81 (0x02 == Integer and 0x81 == 129 bytes long)
modulus: (129 bytes - starts with a null (0x00), remove this.)
00 c7 8a 46 ac b5 cf 3e 23 cd 73 0a 0f ea 59
6f 1d 32 bf 26 aa f5 d0 de a6 cf 02 6b b4 46
3c 68 65 52 38 ee db ec 91 89 45 01 73 9f d2
c3 eb 84 ed a7 52 ea 28 26 78 27 1d 5d 3a df
d8 93 4c 46 06 d6 f7 24 35 a5 b6 47 a5 39 41
37 50 e5 1a b9 bb eb 95 de 93 24 ef 0e d5 b3
89 f7 ba b4 3a 8e 7a ad da b4 d7 6c 2d 43 35
af cf 15 e0 19 6a d6 df ed f7 c1 07 2d 08 18
ed 33 73 5d bc 22 c8 58 73
separator:
02 03 (0x02 == Integer and 0x03 == 3 bytes long)
public exponent: (3 bytes)
01 00 01 (Integer value 65537, Fermat Number F4)
separator:
02 81 81 (0x02 == Integer and 0x81 == 129 bytes long)
private exponent: (129 bytes - starts with a null, remove this)
00 b4 cd 97 62 71 4e fa b8 48 35 bf dd 51 f4
7d 99 10 5d 61 f5 30 cd 74 a1 e3 1b 07 6a 8e
e5 b7 96 6f 5d 45 19 a3 8e ef b9 c6 29 f5 9c
6d 88 1f a7 93 a0 ae a9 78 ca 10 6f 2c 05 e7
c4 7f 1b 72 aa b0 39 1b 45 86 5c 95 eb c5 35
cb 84 7e f1 6c 43 36 1d 1a 7a fc 47 f2 14 52
ff 55 f9 d3 7d 43 26 6d 49 95 4d 04 fa f4 ad
8a 4b 4d d2 d0 b7 79 b1 f9 84 4f b5 3b 16 c8
1d 26 7e 58 e5 8b 61 7e c9
separator:
02 41 (0x02 == Integer and 0x41 == 65 bytes long)
prime1: (65 bytes - starts with a null, remove this)
00 e6 e8 a0 46 02 a9 f1 27 06 6a e5 22 8e f7
4e 2d 92 21 1d 6a bb cb 95 b3 fa 73 87 52 e0
f0 f0 fe f0 39 32 94 df 84 09 02 85 84 7b be
f5 a7 d3 df fc 64 c0 fe 4a f4 05 09 cf 42 f5
94 0f 11 b3 27
separator:
02 41 (0x02 == Integer and 0x41 == 65 bytes long)
prime2: (65 bytes - starts with a null, remove this)
00 dd 39 0b a9 2b c0 f7 ab c8 52 ab 2a d8 ce
18 92 27 88 8a 18 ef 6c 11 9e 83 5c 74 41 2c
dc 70 d1 85 fe 3c 61 61 68 ae 24 5b 67 29 73
cf 33 45 cb f8 26 cd 3e 97 25 04 df 92 d1 aa
ab e1 59 0f d5
separator:
02 40 (0x02 == Integer and 0x40 == 64 bytes long)
exponent1: (64 bytes)
62 09 68 6a f1 1c 98 1f 9a 90 ee 02 13 33 1a
c5 2c 62 d4 eb 89 1a 31 d0 3d 48 a9 ae dd 84
4e bd de de 5a 04 6d 35 d0 e1 7a 30 ba 9d 64
0d 42 5e b9 f9 49 1b 6e 55 56 82 48 b6 44 2f
fd 89 e5 47
separator:
02 41 (0x02 == Integer and 0x41 == 65 bytes long)
exponent2: (65 bytes - starts with a null, remove this)
00 c0 77 73 17 b9 c3 67 37 83 4f b9 2f cb f4
73 18 25 60 fb 94 fa 28 b1 a3 91 72 0c 8a ef
b6 d2 48 d8 24 fa ef 56 4a 36 c7 d6 e6 08 00
83 d2 7d f5 19 6e d8 be 8d cd 5d 52 0e 70 6f
e6 9e 66 58 09
separator:
02 41 (0x02 == Integer and 0x41 == 65 bytes long)
coefficient: (65 bytes - always starts with a null)
00 ba ba e9 9a 9a a3 e6 f8 34 f3 b6 67 80 a7
c5 19 1e 6b a3 30 e2 4e c2 b9 0d c7 93 57 de
ca 6b 76 3e 37 39 7e 5d 64 f1 0c 15 a4 e1 83
e1 d9 99 4a bf 8d 36 85 91 1f 58 16 31 50 39
f9 66 41 ff 6f
Using Linux, the following command generated this public key:
openssl rsa -pubout -in rsa_1024_priv.pem -out rsa_1024_pub.pem
-----BEGIN PUBLIC KEY----- MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDHikastc8+I81zCg/qWW8dMr8m qvXQ3qbPAmu0RjxoZVI47tvskYlFAXOf0sPrhO2nUuooJngnHV0639iTTEYG1vck NaW2R6U5QTdQ5Rq5u+uV3pMk7w7Vs4n3urQ6jnqt2rTXbC1DNa/PFeAZatbf7ffB By0IGO0zc128IshYcwIDAQAB -----END PUBLIC KEY-----
Parts in bold, in order:
-----BEGIN PUBLIC KEY-----
30 81 9f 30 0d 06 09 2a 86 48 86 f7 0d 01 01 01 05 00 03 81 8d 00
30 81 89 02 81 81 00 c7 8a 46 ac b5 cf 3e 23 cd 73 0a 0f ea 59 6f
1d 32 bf 26 aa f5 d0 de a6 cf 02 6b b4 46 3c 68 65 52 38 ee db ec
91 89 45 01 73 9f d2 c3 eb 84 ed a7 52 ea 28 26 78 27 1d 5d 3a df
d8 93 4c 46 06 d6 f7 24 35 a5 b6 47 a5 39 41 37 50 e5 1a b9 bb eb
95 de 93 24 ef 0e d5 b3 89 f7 ba b4 3a 8e 7a ad da b4 d7 6c 2d 43
35 af cf 15 e0 19 6a d6 df ed f7 c1 07 2d 08 18 ed 33 73 5d bc 22
c8 58 73 02 03 01 00 01
-----END PUBLIC KEY-----
header:
30 81 9f 30 0d 06 09 2a 86 48 86 f7 0d 01 01
01 05 00 03 81 8d 00 30 81 89
separator:
02 81 81
modulus:
00 c7 8a 46 ac b5 cf 3e 23 cd 73 0a 0f ea 59
6f 1d 32 bf 26 aa f5 d0 de a6 cf 02 6b b4 46
3c 68 65 52 38 ee db ec 91 89 45 01 73 9f d2
c3 eb 84 ed a7 52 ea 28 26 78 27 1d 5d 3a df
d8 93 4c 46 06 d6 f7 24 35 a5 b6 47 a5 39 41
37 50 e5 1a b9 bb eb 95 de 93 24 ef 0e d5 b3
89 f7 ba b4 3a 8e 7a ad da b4 d7 6c 2d 43 35
af cf 15 e0 19 6a d6 df ed f7 c1 07 2d 08 18
ed 33 73 5d bc 22 c8 58 73
separator:
02 03
public exponent:
01 00 01