Cryptographic keys for security should be generated by true random number generators that apply irreversible hashing algorithms to initial values taken from a random source. As DRAM shows randomness in its access latency, it can be used as a random source. However, systems with synchronous DRAM (SDRAM) do not easily expose such randomness resulting in highly clustered random numbers. We resolved this problem by using the xor instruction. Statistical testing shows that the generated random bits have the quality comparable to true random bit sequences. The performance of bit generation is at the order of 100 Kbits/sec. Since the proposed random number generation requires neither external devices nor any special circuits, this method may be used in any computing device that employs DRAM.