Definition of textbook RSA What is the definition of textbook or "raw" RSA?

What are some of the properties of textbook RSA?

How does it differ from other schemes based on RSA?
Textbook RSA:

Choose two large primes $p$ and $q$.
Let $n=p\cdot q$. Choose $e$ such that $gcd(e,\varphi(n))=1$ (where $\varphi(n)=(p-1)\cdot (q-1)$). Find $d$ such that $e\cdot d\equiv 1\bmod{\varphi(n)}$. In other words, $d$ is the modular inverse of $e$, ($d\equiv e^{-1}\bmod{\varphi(n)}$).

$(e, n)$ is the public key, $(d, n)$ the private one.


To encrypt a message $m$, compute $c\equiv m^e\mod n$.
To decrypt a ciphertext $c$, compute $m \equiv c^d\mod n$.


Signing and verifying messages is also defined (omitted for brevity).

Some (Undesirable) Properties of Textbook RSA:


It is malleable. I.e., if you give me a ciphertext $c$ which encrypts $m$, I can compute $c'\equiv c\cdot 2^e\mod n$. When the owner of the private key decrypts $c'$, she will get $2m\mod n$. In other words, I can make predictable changes to ciphertexts.
It is deterministic, and thus not semantically secure. I.e., I can distinguish between the encryptions of $0$ and $1$ (simply by encrypting both values myself and comparing the ciphertexts).


Differences with Deployed RSA:


Padding
Chinese Remainder Theorem is sometimes used in deployed systems for more efficient decryption.
$e$ is often statically set to $65537 = 2^{16} + 1$ for encryption speed (since there are only two set bits in that number).
Side-channel attack mitigations can be put in place for deployed systems too.


In no way is my list comprehensive, but hopefully this helps.