Rayden Cryptosystem is a suite of cryptographic hash, private/public key generator, and cipher algorithms for both symmetric and asymmetric encryption. Rayden features 4096-bit length keys; 256/512/1024/2048-bit length, 118/296/716/1684-bit dynamically addressed blocks; and 16-bit dynamically addressed chaining. Rayden is designed with cryptographic primitives not utilized by any other cryptosystem. The trapdoor one-way function implemented in the asymmetric cipher is demonstrably NP-complete.