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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> Are there efficient attacks against such an implementation?
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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 $d$.
Yes, you can use small public exponents (e.g., 3 is fine), as long as you never encrypt the same plaintext under three or more RSA public keys with exponent 3. Otherwise, there is "Hastad's broadcast attack" that can extract the plaintext, without needing to factor the modulus. 

Also, ensure that the private exponent is large enough, as pointed out Jason S (which will usually be the case, if primes are chosen randomly).