A new stream ciphering technique based on multiplicative polynomial inverses over Galois Field GF(73) is proposed, where a set of randomly generated key-bytes, between 1 and 15, is dynamically permuted and XORed with the identical number of message bytes. The output cipher is tested using NIST Statistical Test Suite and results are compared with that obtained by the well-known RC4 stream cipher. The new cipher is statistically random and observed to be better than RC4. © Springer India 2016.