Efficiency Analysis of Arithmetic for Public-Key Cryptosystems and its Applications

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We have investigated the following research topics.(1) For a countermeasure against side channel attacks on Koblitz curve cryptosystem, we proposed a tau expansion with a fixed pattern for a give element in an imaginary quadratic filed.(2) A secret bit of a scalar multiplication in PKC corresponds to either a multiplication or a squaring. We experimented that a multiplication with two same input has a different power consumption.(3) XTR is one of the most efficient public-key cryptosystems. We presented an algorithm that computes an exponentiation with a fixed pattern secure against side channel attacks.(4) RSA-CRT is an efficient method to enhance the speed of RSA cryptosystem. We gave a survey of RSA-CRT and some countermeasures against side channel attacks.(5) The final exponentiation of pairing on supersingular elliptic curve over finite field with characteristic three was improved by 50% using the torus over GF (3^m).E(6) CDSA requires a multi-scalar multiplication in the verification step. In this research we presented a minimal joint Hamming weight class for a window method using Shamir's trick.(7) We proposed a variant of XTR over GF (3^6m) whose ciphertexts can be compressed by 1/6. We also presented an efficient implementation using the optimal normal basis (ONB).(8) We have presented an efficient representation of scalar by the Frobenius map of Koblitz curve, which is able to reduce the number of pre-computed table only to two in TNAF5.(9) We proposed an efficient implementation of EtaT pairing using the random coordinate secure against side channel attacks.(10) We published a proceedings of the first conference on pairing-based cryptography "Pairing 2007", which deals basic mathematics, cryptographic protocols, implementation, and applied security, related to pairing.