• Journal of the Institute of Convergence Signal Processing
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• v.11 no.3
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• pp.244-249
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• 2010

The design of error correction code with low complexity has a good attraction for next generation multi-level cell flash memory. Sharing sub-expressions is effective method to reduce complexity and chip size. This paper proposes a new design method of m-bit parallel BCH encoder based on serial linear feedback shift register structure with low complexity using sub-expression. In addition, general algorithm for obtaining the sub-expression is introduced. The sub-expression can be expressed by matrix operation between sub-matrix of generator matrix and sum of two different variables. The number of the sub-expression is restricted by. The obtained sub-expressions can be shared for implementation of different m-parallel BCH encoder. This paper is not focused on solving a problem (delay) induced by numerous fan-out, but complexity reduction, expecially the number of gates.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.5
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• pp.17-30
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• 2001

In this paper, we implemented a scalar multiplier needed at an elliptic curve cryptosystem over standard basis in $GF(2^{163})$. The scalar multiplier consists of a radix-16 finite field serial multiplier and a finite field inverter with some control logics. The main contribution is to develop a new fast finite field inverter, which made it possible to avoid time consuming iterations of finite field multiplication. We used an algorithmic transformation technique to obtain a data-independent computational structure of the Extended Euclid GCD algorithm. The finite field multiplier and inverter shown in this paper have regular structure so that they can be easily extended to larger word size. Moreover they can achieve 100% throughput using the pipelining. Our new scalar multiplier is synthesized using Hyundai Electronics 0.6$\mu\textrm{m}$ CMOS library, and maximum operating frequency is estimated about 140MHz. The resulting data processing performance is 64Kbps, that is it takes 2.53ms to process a 163-bit data frame. We assure that this performance is enough to be used for digital signature, encryption & decryption and key exchange in real time embedded-processor environments.