Question: Just to establish notation with respect to the RSA protocol, let $n = pq$ be the product of two large primes and let $e$ and $d$ be the public and private exponents, respectively ($e$ is the inverse of $d \bmod \varphi(n)$). Given a plaintext message $m$, we obtain the ciphertext $c = m^e \bmod n$; we subsequently decrypt the ciphertext by calculating $c^d \bmod n$.

Suppose I'm trying to implement RSA on a device with low computational power, and these exponentiations take too long. I decide to make my implementation run faster by choosing small values for $e$ and $d$ (e.g. in the tens or hundreds). 

**Are there efficient attacks against such an implementation?**

Answer: 
You need to read some recent papers and their references to get up to speed with these attacks. Try ["New Weak RSA Keys"](http://www.math.unicaen.fr/~nitaj/rsa12.pdf) by Nitaj and ["Revisiting Wiener's Attack – New Weak Keys in RSA"](http://eprint.iacr.org/2008/228.pdf) by Maitra and Sarkar

Note that if you're trying to speed things up then there are almost certainly better solutions than trying to keep the exponents small.
$e$ and $d$ *cannot* both be small, because $ed$ must equal at least $(p-1)(q-1)+1$, which is very large if the scheme is to provide any security against factoring algorithms.