A high-speed square root algorithm in extension fields
ICISC'06 Proceedings of the 9th international conference on Information Security and Cryptology
Implementing cryptographic pairings
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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This paper focuses on developing a square root (SQRT) algorithm in finite fields GF(p2d) (d â聣楼 0). Examining the Smart algorithm, a well-known SQRT algorithm, we can see that there is some computation overlap between the Smart algorithm and the quadratic residue (QR) test, which must be implemented before a SQRT computation. It makes the Smart algorithm inefficient. In this paper, we propose a new QR test and a new SQRT algorithm in GF(p2d), in which not only there is no computation overlap, but also most of computations required for the proposed SQRT algorithm in GF(p2d) can be implemented in the corresponding subfields GF(p2d-i) for 1 â聣陇 i â聣陇 d, which yields many reductions in the computational time and complexity. The computer simulation also shows that the proposed SQRT algorithm is much faster than the Smart algorithm.