Decrypt from cipher text encrypted using RSA

Start with saving the three parts respectively to pub.b64, priv.b64 and blob.b64:

$ base64 -d < pub.b64 | openssl asn1parse -inform DER -i

    0:d=0  hl=3 l= 158 cons: SEQUENCE
    3:d=1  hl=2 l=  13 cons:  SEQUENCE
    5:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
   16:d=2  hl=2 l=   0 prim:   NULL
   18:d=1  hl=3 l= 140 prim:  BIT STRING

Clearly not an X.509v3 certificate. No matter, we don't need that to decrypt. openssl dumpasn1 isn't up to the heavy lifting here, try Peter Gutmann's dumpasn1 to peek inside the bit string:

$ base64 -d < pub.b64 > pub.der
$ dumpasn1 -al pub.der

   0  158: SEQUENCE {
   3   13:   SEQUENCE {
   5    9:     OBJECT IDENTIFIER rsaEncryption (1 2 840 113549 1 1 1)
         :       (PKCS #1)
  16    0:     NULL
         :     }
  18  140:   BIT STRING, encapsulates {
  22  136:     SEQUENCE {
  25  128:       INTEGER
         :         77 C8 9B 9A 58 AC 43 14 B8 95 1E BE 61 03 E9 B5
         :         05 C7 CA 7D 1B FE 6F 17 E8 9A F9 09 EB 9F C3 9E
         :         32 92 09 FC A4 B6 9E A0 CB C5 7C 7F 7B 33 4A 94
         :         50 2B 58 AD 56 7A BE 1D 8B 04 09 D9 C7 62 0A A3
         :         68 AE E6 C0 82 73 97 31 5F BF 16 C8 80 4D 08 CC
         :         4F 61 36 94 8F 71 51 6A AA 36 AF 8F 7E 0C 82 3C
         :         82 D1 96 23 47 4F F8 F6 A8 EB C0 38 79 9F DD AD
         :         5D 3F C9 5C A6 FC 37 C7 71 41 04 AA 6A B7 3A 89
 156    3:       INTEGER 65537
         :       }
         :     }
         :   }

That's more like it, we have what appears to be a 1024-bit modulus, and a likely public exponent of 65537.

The key is a base64 encoded normal RSA key in DER (binary) format:

$ base64 -d priv.b64 | openssl rsa -inform DER > out.key
writing RSA key
$ cat out.key
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

If you decode that key:

$ openssl asn1parse  < out.key
    0:d=0  hl=4 l= 600 cons: SEQUENCE          
    4:d=1  hl=2 l=   1 prim: INTEGER           :00
    7:d=1  hl=3 l= 128 prim: INTEGER           
                      :77C89B9A58AC4314B8951EBE6103E9B505C7CA7D1BFE6F17E89AF9
                       09EB9FC39E329209FCA4B69EA0CBC57C7F7B334A94502B58AD567A
                       BE1D8B0409D9C7620AA368AEE6C0827397315FBF16C8804D08CC4F
                       6136948F71516AAA36AF8F7E0C823C82D19623474FF8F6A8EBC038
                       799FDDAD5D3FC95CA6FC37C7714104AA6AB73A89
  138:d=1  hl=2 l=   3 prim: INTEGER           :010001
  [...snip...]

and compare with the dumpasn1 decoding of the public key, you can see that they share a 1024 bit modulus and exponent, so it looks like the public and private key match. Good.

So, decode your encrypted data:

$ base64 -d blob.b64 > blob

and decrypt it:

$ openssl rsautl -decrypt -inkey out.key < blob > decrypted
$ hexdump decrypted
0000000 0355 1739 575b 5434 ccc5 bec7 e70a 0d44
0000010 a4a9 11d4 166c 3423 4e36 e657 2fea ef53

That's 32 bytes (256 bits), quite likely a key used in a symmetric cipher to encrypt more data, since you can only encrypt relatively small amounts of data with RSA

Good luck with the next part ;-)

After decoding the strings from base64 to binary, you should try the following, depending on the algorithm used.

This encodes from base64 to binary. You probably would have to do it with the keys, too (or just decode them manually)

$ openssl enc -in ciphertext -out binarytext -d -a

And to perform the decryption:

$ openssl rsautl -decrypt -in binarytext -out plaintext -inkey private.pem