Prime Numbers in Discrete Log

I am implementing a security protocol based on discrete log. I came across the equation $p = kq + 1$. Understand that based on number theories that both $p$ and $q$ should be large enough to be "safe". However, how does it justifies safe? Say I chose $p = 7$, $k = 2$ and $q = 3$, will my implementation be screwed up?

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You have chosen the tag "dsa", but there is no mention of digital signatures in your question. Do you need primes for Diffie-Hellman or for a signature scheme? –  Henrick Hellström Dec 26 '14 at 19:02

The smallest prime in the former set is 1536 bits, which means that it is greater than $2^{1535}$. It is recommended to be used with a 180 bit exponent, which corresponds to an integer greater than $2^{179}$.