Nowadays, the chaotic cryptosystems are gaining more attention due to their efficiency, the assurance of robustness and high sensitivity corresponding to initial conditions. In literature, on one hand there are many encryption algorithms that only guarantee security while on the other hand there are schemes based on chaotic systems that only promise the uncertainty. Due to these limitations, each of these approaches cannot adequately encounter the challenges of current scenario. Here we take a unified approach and propose an image encryption algorithm based on Lorenz chaotic system and primitive irreducible polynomial S-boxes. First, we propose 16 different S-boxes based on projective general linear group and 16 primitive irreducible polynomials of Galois field of order 256, and then utilize these S-boxes with combination of chaotic map in image encryption scheme. Three chaotic sequences can be produced by the Lorenz chaotic system corresponding to variables $x$, $y$ and $z$. We construct a new pseudo random chaotic sequence $k_i$ based on $x$, $y$ and $z$. The plain image is encrypted by the use of chaotic sequence $k_i$ and XOR operation to get a ciphered image. To demonstrate the strength of presented image encryption, some renowned analyses as well as MATLAB simulations are performed.