This is an RSA key

-----BEGIN RSA PRIVATE KEY-----
MIGtAgEAAiEA5tygpSZdOZUMfuO3oTGWR4cALBtWui5UzrQw2/8JlZ0CAwEAAQIh
AI9n4Yp1KFfKlHaF8d15tgUONQXn+e3aI+beFKoi2XipAhEA/ZkHPmcDwXIqloGr
minb1wIRAOkMdv7emMGd08gwwOQ6i6sCEQC0pjcXx9BQFCCsWDDCwAC/AhEAxYcn
JQeO+izH4JpSJB/rWQIRAOO9m6JHEWgzLYD+fe003vw=
-----END RSA PRIVATE KEY-----

It was generated with the command $ openssl genrsa 256. A secret 64 bit number was encrypted with this key, resulting in this cipher text

6794893f3c47247262e95fbed846e1a623fc67b1dd96e13c7f9fc3b880642e42

Recover the secret number (in lowercase hex).

Test Vector

Here are some numbers and their associated ciphertexts when encrypted with the given key.

64 -> 71b71b4f55ba6c921c33fbe91f51bf888bba9761134c2ac6456e02f3802b1b69
6e -> 842129370f36e80ca715b4cd97570d7a664f8def2c22f580866b04aeaa87fef2
78 -> c6128c44895959192315ffc715ef2dd9feaddd25b297696da01d5c3dbfc9cb4b
82 -> 432beb994a0aef57e61822b1e89c2afa41663ddf9928922ae932894329a1e208
8c -> bed8d61a863a430b7c11bb71220db0ed9f605bdfca5c86b202e0b5b021272eb5
96 -> 3c67f8d506f637b8d447a4f4568e1d0eb27de62db3ff3ea9b93011c35b1e387
a0 -> c1ade6db41c134eb2cf649366368286dc768462aefad58b17018cad5b65de4
aa -> 6d2b3c8cf668777e981b9f6690c16a3b0aee07e16aed8a0ab59883671925d855
b4 -> 5e711cd1cdfd3a09429ca06ed16217b8951552c467329d9cebd936f792503329
be -> 7fa80734ec297b4f5dd50a14a0981d2ebcf8f19561f43878b49a9774fea00965

Solution