My doubt is, when JDK 7 already has JCE JARs, why should I specifically download the same JCE JARs and replace the existing JCE JARs again..??
No. Or at least, not without understanding what the JCE error means.
If you showed us the error messages / stacktraces, maybe we could help you with that.
UPDATE
Those errors look like problems in your code rather than in JCE.
SSHA stands for Salted SHA. SSH / SSHA are secure hash schemes, not an encryption schemes. Moreover, you won't find a JCE provider for SSHA ... because it is really just a variation on SHA where you add a "salt" to the input that you are hashing.
The "illegal key size" exception looks like you are misusing one of the API methods.
If you showed us the code that throws the exceptions ... and the full stacktraces ... we could give you a more definite answer. But I'm convinced that replacing the JCE JARs will make no difference.