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4

First, the advice: What are the best-practices to store the message length / strip away padding? Use standard padding, like PKCS#7 padding. It handles finding the length uniquely for you. Use encrypt-then-MAC to prevent padding oracle attacks. (Or better yet, don't use CBC. Use an authenticated encryption mode like GCM, or use CTR+MAC which doesn't ...

2

Yes, and it's devastatingly effective, too. See OAEP and other RSA/asymmetric-function padding standards. OAEP is what you should use these days so far as I am aware. PKCS#1 has other defined padding schemes also (eg PSS, PKCS1.5), only some of which are effective.

2

If you were using $e=3$, then there is a well known attack by Bleichenbacher that enables the trivial generation of a signature that passes verification. This attack was never published, but is described here. Note that this attack appeared in a real vulnerability in Kindle (and some versions of Android). In any case, the attack does not work for $e=65536$. ...

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