This paper presents a new trapdoor-knapsack public-key-cryptosystem. The encryption equation is based on the general modular knapsack equation, but unlike the Merkle-Hellman scheme the knapsack components do not have to have a superincreasing structure. The trapdoor is based on transformations between the modular and radix form of the knapsack components, via the Chinese Remainder Theorem. The resulting cryptosystem has high density and has a typical message block size of 2000 bits and a public key of 14K bits. The security is based on factoring a number composed of 256 bit prime factors. The major advantage of the scheme when compared with the RSA scheme is one of speed. Typically, knapsack schemes cuch as the one proposed here are capable of throughput speeds which are orders of magnitude faster than the RSA scheme.