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.
Even if your computing power is small, you can use larger exponents. There are some algorithms such as [repeated squaring method](http://www.algorithmist.com/index.php/Repeated_Squaring) which help you to compute larger exponents a lot faster than brute force.

Repeated squaring method can also be applied in RSA by building up one bit at a time, so we can double the exponent of a number in one go. So the number of multiplication we have to make is log n (where n is an exponent) compared to n multiplications for normal computation of exponent of the number.