Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three
IEEE Transactions on Computers
A Fault Attack on Pairing-Based Cryptography
IEEE Transactions on Computers
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
A Reconfigurable Processor for the Cryptographic nT Pairing in Characteristic 3
ITNG '07 Proceedings of the International Conference on Information Technology
An Algorithm for the nt Pairing Calculation in Characteristic Three and its Hardware Implementation
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Side channel analysis of practical pairing implementations: which path is more secure?
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
Implementing cryptographic pairings on smartcards
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Hardware acceleration of the tate pairing in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
IEEE Transactions on Information Theory
The importance of the final exponentiation in pairings when considering fault attacks
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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Pairing-based cryptosystems have been widely researched, and several efficient hardware implementations of pairings have also been proposed. However, side channel attacks (SCAs) are serious attacks on hardware implementations. Whelan et al. pointed out that pairings except the ηT pairing might not be vulnerable against SCAs by setting the secret point to the first parameter [25]. This paper deals with SCAs for the ηT pairing over F3n. To our knowledge, the randomized-projective-coordinate method has the smallest overhead among all countermeasures against SCAs for the ηT pairing. The cost of that overhead is 3nM, where M is the cost of a multiplication in F3n. In this paper, we propose another countermeasure based on random value additions (xp + λ) and (yp + λ), where P = (xp, yp) is the input point, and λ is a random value in F3n. The countermeasure using the random value addition was relatively slow in the case of the scalar multiplication of elliptic curve cryptosystems. However, in the case of the ?T pairing, we can construct an efficient countermeasure due to the form of the function gP(x, y) = yp3y-(xp3 + x - 1)2 for a point P = (xp, yp). The overhead of our proposed scheme is just 0.5nM, which is a reduction of more than 75% compared with the randomized-projective-coordinate method.