[encryption] RSA Public Key format

Starting from the decoded base64 data of an OpenSSL rsa-ssh Key, i've been able to guess a format:

• 00 00 00 07: four byte length prefix (7 bytes)
• 73 73 68 2d 72 73 61: "ssh-rsa"
• 00 00 00 01: four byte length prefix (1 byte)
• 25: RSA Exponent (e): 25
• 00 00 01 00: four byte length prefix (256 bytes)

• RSA Modulus (n):

  7f 9c 09 8e 8d 39 9e cc d5 03 29 8b c4 78 84 5f
  d9 89 f0 33 df ee 50 6d 5d d0 16 2c 73 cf ed 46 
  dc 7e 44 68 bb 37 69 54 6e 9e f6 f0 c5 c6 c1 d9 
  cb f6 87 78 70 8b 73 93 2f f3 55 d2 d9 13 67 32 
  70 e6 b5 f3 10 4a f5 c3 96 99 c2 92 d0 0f 05 60 
  1c 44 41 62 7f ab d6 15 52 06 5b 14 a7 d8 19 a1 
  90 c6 c1 11 f8 0d 30 fd f5 fc 00 bb a4 ef c9 2d 
  3f 7d 4a eb d2 dc 42 0c 48 b2 5e eb 37 3c 6c a0 
  e4 0a 27 f0 88 c4 e1 8c 33 17 33 61 38 84 a0 bb 
  d0 85 aa 45 40 cb 37 14 bf 7a 76 27 4a af f4 1b 
  ad f0 75 59 3e ac df cd fc 48 46 97 7e 06 6f 2d 
  e7 f5 60 1d b1 99 f8 5b 4f d3 97 14 4d c5 5e f8 
  76 50 f0 5f 37 e7 df 13 b8 a2 6b 24 1f ff 65 d1 
  fb c8 f8 37 86 d6 df 40 e2 3e d3 90 2c 65 2b 1f 
  5c b9 5f fa e9 35 93 65 59 6d be 8c 62 31 a9 9b 
  60 5a 0e e5 4f 2d e6 5f 2e 71 f3 7e 92 8f fe 8b
  

The closest validation of my theory i can find it from RFC 4253:

The "ssh-rsa" key format has the following specific encoding:

  string    "ssh-rsa"
  mpint     e
  mpint     n

Here the 'e' and 'n' parameters form the signature key blob.

But it doesn't explain the length prefixes.

Taking the random RSA PUBLIC KEY i found (in the question), and decoding the base64 into hex:

30 82 01 0a 02 82 01 01 00 fb 11 99 ff 07 33 f6 e8 05 a4 fd 3b 36 ca 68 
e9 4d 7b 97 46 21 16 21 69 c7 15 38 a5 39 37 2e 27 f3 f5 1d f3 b0 8b 2e 
11 1c 2d 6b bf 9f 58 87 f1 3a 8d b4 f1 eb 6d fe 38 6c 92 25 68 75 21 2d 
dd 00 46 87 85 c1 8a 9c 96 a2 92 b0 67 dd c7 1d a0 d5 64 00 0b 8b fd 80 
fb 14 c1 b5 67 44 a3 b5 c6 52 e8 ca 0e f0 b6 fd a6 4a ba 47 e3 a4 e8 94 
23 c0 21 2c 07 e3 9a 57 03 fd 46 75 40 f8 74 98 7b 20 95 13 42 9a 90 b0 
9b 04 97 03 d5 4d 9a 1c fe 3e 20 7e 0e 69 78 59 69 ca 5b f5 47 a3 6b a3 
4d 7c 6a ef e7 9f 31 4e 07 d9 f9 f2 dd 27 b7 29 83 ac 14 f1 46 67 54 cd 
41 26 25 16 e4 a1 5a b1 cf b6 22 e6 51 d3 e8 3f a0 95 da 63 0b d6 d9 3e 
97 b0 c8 22 a5 eb 42 12 d4 28 30 02 78 ce 6b a0 cc 74 90 b8 54 58 1f 0f 
fb 4b a3 d4 23 65 34 de 09 45 99 42 ef 11 5f aa 23 1b 15 15 3d 67 83 7a 
63 02 03 01 00 01

From RFC3447 - Public-Key Cryptography Standards (PKCS) #1: RSA Cryptography Specifications Version 2.1:

A.1.1 RSA public key syntax

An RSA public key should be represented with the ASN.1 type RSAPublicKey:

  RSAPublicKey ::= SEQUENCE {
     modulus           INTEGER,  -- n
     publicExponent    INTEGER   -- e
  }

The fields of type RSAPublicKey have the following meanings:

• modulus is the RSA modulus n.
• publicExponent is the RSA public exponent e.

Using Microsoft's excellent (and the only real) ASN.1 documentation:

30 82 01 0a       ;SEQUENCE (0x010A bytes: 266 bytes)
|  02 82 01 01    ;INTEGER  (0x0101 bytes: 257 bytes)
|  |  00          ;leading zero because high-bit, but number is positive
|  |  fb 11 99 ff 07 33 f6 e8 05 a4 fd 3b 36 ca 68 
|  |  e9 4d 7b 97 46 21 16 21 69 c7 15 38 a5 39 37 2e 27 f3 f5 1d f3 b0 8b 2e 
|  |  11 1c 2d 6b bf 9f 58 87 f1 3a 8d b4 f1 eb 6d fe 38 6c 92 25 68 75 21 2d 
|  |  dd 00 46 87 85 c1 8a 9c 96 a2 92 b0 67 dd c7 1d a0 d5 64 00 0b 8b fd 80 
|  |  fb 14 c1 b5 67 44 a3 b5 c6 52 e8 ca 0e f0 b6 fd a6 4a ba 47 e3 a4 e8 94 
|  |  23 c0 21 2c 07 e3 9a 57 03 fd 46 75 40 f8 74 98 7b 20 95 13 42 9a 90 b0 
|  |  9b 04 97 03 d5 4d 9a 1c fe 3e 20 7e 0e 69 78 59 69 ca 5b f5 47 a3 6b a3 
|  |  4d 7c 6a ef e7 9f 31 4e 07 d9 f9 f2 dd 27 b7 29 83 ac 14 f1 46 67 54 cd 
|  |  41 26 25 16 e4 a1 5a b1 cf b6 22 e6 51 d3 e8 3f a0 95 da 63 0b d6 d9 3e 
|  |  97 b0 c8 22 a5 eb 42 12 d4 28 30 02 78 ce 6b a0 cc 74 90 b8 54 58 1f 0f 
|  |  fb 4b a3 d4 23 65 34 de 09 45 99 42 ef 11 5f aa 23 1b 15 15 3d 67 83 7a 
|  |  63 
|  02 03          ;INTEGER (3 bytes)
|     01 00 01

giving the public key modulus and exponent:

• modulus = 0xfb1199ff0733f6e805a4fd3b36ca68...837a63
• exponent = 65,537

Update: My expanded form of this answer in another question