Is it possible to get the RSA secret key, knowing the public key and the set of records "source data => encrypted data"?

Question

I am working on apllication, which allows plugins to access different sets of functions, each plugin provides an “initialization string” that sets the level of access to various functions. The developers send me these lines, and I encrypt them using my 1024-bit RSA private key and send the encoded data back. When launched, my application decodes the encoded data (encoded initialization string) using the built-in public key and if "decoded data! = Initialization string" does not start.

So, is it possible to use the database “initialization string” => “encoded initialization string” (extracted from other plugins) to crack my private key, or make it possible to force use it in a reasonable amount of time?

Answer 1

, " RSA", . . , , - , . - , RSA " " . (, -), , .

RSA (, PKCS # 1, 8 " " ) RSA- (1024 ), , , , , , (, , RSA). , , 30 .

, , ( , , , , ​​RSA), ; . PKCS # 1 ( "v1.5" ) . "ISO 9796" , .

(.. PKCS # 1), . . , RSA ( /) PKCS # 1.

Answer 2

, RSA1024.

, , RSA- , , , , - , RSA, , , .

, RSA , .

, (, DES), .

Answer 3

The whole point of RSA's public / private key technology is that it is very difficult to reverse.

Cracks are known that exploit some specific implementation flaws, but it is believed that the basic algorithm takes decades to yield to brute force attack. See this .