Graduate Thesis Or Dissertation
 

Side channel attack resistant elliptic curves cryptosystem on multi-cores for power efficiency

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  • The Advent of multi-cores allows programs to be executed much faster than before. Cryptoalgorithms use long-bit words thus parallelizing these operations on multi-cores will achieve significant performance improvement. However, not all long-bit word operations in cryptosystems are suitable for parallel execution on multi-cores. In particular, long-bit words used in Elliptic Curves Cryptography (ECC) do not efficiently divide by the system word size. This causes some of the cores to be idle, which makes it vulnerable for attackers to guess how many operations occurred and thus what field size is being used. Multiplication is the most important part of public key cryptosystems. Long-bit word multiplication operations are needed for encryption and decryption. J. Fan et al. proposed using Montgomery multiplication on multi-cores using GF(2²⁵⁶) [25, 26], which is suitable for comput-er systems with 16-bit or 32-bit word size. Fan‟s Montgomery multiplication is suitable for most RSA. However, in ECC, some GFs will cause idle cores. For example, suppose GF(2¹³¹) is used (which is one of the recommended word size by NIST) on a quad-core with a 32-bit word size, which requires [132/32] =5 iterations with the last iteration requiring just a 3-bit operation. This cause three of the cores to be idle during this time causing needless power consumption. The most general and the easiest way to make side channel attacks difficult is to insert dummy instructions to cover the idle processors. However, dummy instructions result in extra workloads that lead to performance degradation and increases in power consumption. In this thesis, we will present a multiplier adjuster technique to improve the execution time and the power consumption for the last unbalanced iteration. By appropriately applying dummy instructions between point-addition and point-doubling operations, a balanced point operation can be achieved in ECC. The performance and power-efficiency of the proposed method on multi-cores are analyzed for each GF used in ECC.
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