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: 
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Yes. You need to keep $d$ larger than the 4th root of $n=pq$. Otherwise [Wiener's Attack](http://en.wikipedia.org/wiki/Wiener%27s_Attack) can be used to compute $d$.
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.