A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations applied to a message ($M$) yields the encrypted message ($M_E$). In that series of operations, the one with the most important role is operation 6, which involves a random binary sequence (RBS) generated by using the Hybrid Random Number Generator (HRNG) or the Mathematical Random Number Generator (MRNG). A sequence of anti-operations applied to $M_E$ makes it possible to recover $M$.