We describe the implementation of an elliptic curve cryptographic (ECC) coprocessor over GF (2 m) on an FPGA and also the result of simulations evaluating its LSI implementation. This coprocessor is suitable for server systems that require efficient ECC operations for various parameters. For speeding-up an elliptic scalar multiplication, we developed a novel configuration of a multiplier over GF (2 m), which enables the multiplication of any bit length by using our data conversion method. The FPGA implementation of the coprocessor with our multiplier, operating at 3 MHz, takes 80 ms for 163-bit elliptic scalar multiplication on a pesudo-random curve and takes 45 ms on a Koblitz curve. The 0.25 µm ASIC implementation of the coprocessor, operating at 66 MHz and having a hardware size of 165 Kgates, would take 1.1 ms for 163-bit elliptic scalar multiplication on a pesudo-random curve and would take 0.65 ms on a Koblitz curve.

We propose new fast implementation method of public-key cryptography suitable for DSP. We improved modular multiplication and elliptic doubling to increase speed. For modular multiplication, we devised a new implementation method of Montgomery multiplication, which is suitable for pipeline processing. For elliptic doubling, we devised an improved computation for the number of multiplications and additions.We implemented RSA, DSA and ECDSA on the latest DSP (TMS320C6201, Texas Instruments), and achieved a performance of 11.7 msec for 1024bit RSA signing, 14.5 msec for 1024-bit DSA verification and 3.97 msec for 160-bit ECDSA verification.

We propose three differential power analysis (DPA) countermeasures for securing the public key cryptosystems. All countermeasures are based on the window method, and can be used in both RSA and elliptic curve cryptosystems (ECC). By using the optimal countermeasure, performance penalty is small. In comparison with k-ary method, computation time of our countermeasure is only 105% in 1024-bit RSA and 119% in 160-bit ECC.

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