In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of (1/4)… (More)

ID/password-based authentication is commonly used in network services. Some users set different ID/password pairs for different services, but other users reuse a pair of ID/password to other… (More)

A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, αG in an additive cyclic group generated by an element G of prime order r, and a positive integer d… (More)

In Elliptic Curve Cryptosystems (ECC), a scalar multiplication of a base point is the most time-consuming operation. Thus, a lot of improvemnets on the scalar multiplication algorithms have been… (More)

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, αG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r − 1.… (More)

Barreto–Naehrig (BN) curve has been introduced as a pairing-friendly elliptic curve over prime field Fp which has embedding degree 12. Characteristic and Frobenius trace are given as polynomials of… (More)