CAIRN: Dedicated Integer Factoring Devices

The integer factoring problem is known as one of the hard problem in cryptology, and some public-key cryptosystems including RSA are designed based of this fact. Recently, several dedicated integer factoring devices have been proposed, however, no implementational or even experimental results are not shown. This paper proposes a novel design of a dedicated integer factoring device. In order to verify the do ability of the design, we actually developed the dedicated integer factoring devices CAIRN 1, 2 and 3. CAIRN 1 is the first and concept proof device implemented on DAP-DNA2, while CAIRN 2 is implemented on Xilinx´s FPGA and succeeded factoring a 128-bit composite integer whose factor was unknown at that time. CAIRN 3 is also implemented on Xilinx´s FPGA, and is about 38 times faster than CAIRN 2 in the experimental sieving for a 768-bit integer (RSA 768). It is estimated that the full sieving for RSA 768 requires about 270 years with single CAIRN 3.