Yumi Sakemi

Skew Frobenius Map and Efficient Scalar Multiplication for Pairing---Based Cryptography

This paper considers a new skew Frobenius endomorphism with pairing---friendly elliptic curve

Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve

E(\mathbb{F}{p}{})

Solving DLP with auxiliary input over an elliptic curve used in TinyTate library

defined over prime field

Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing

\mathbb{F}{p}{}

A Spoofing Attack against a Cancelable Biometric Authentication Scheme

. Then, using the new skew Frobenius map, an efficient scalar multiplication method for pairing---friendly elliptic curve

An Improvement of Twisted Ate Pairing with BarretoNaehrig Curve by Using Frobenius Mapping

E(\mathbb{F}{p}{})

Faster Scalar Multiplication for Elliptic Curve Cryptosystems

is shown. According to the simulation result, a scalar multiplication by the proposed method with multi---exponentiation technique is about 40% faster than that by plain binary method.

Accelerating Cross Twisted Ate Pairing with Ordinary Pairing Friendly Curve of Composite Order That Has Two Large Prime Factors

A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G , αG , α d G in an additive cyclic group generated by an element G of prime order r , and a positive integer d satisfying d |(r −1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheons algorithm). This paper reports our experimental results of Cheons algorithm by implementing it with some speeding-up techniques. In fact, we have succeeded to solve DLPwAI on a pairing-friendly elliptic curve of 160-bit order in 1314 core days. Implications of our experiments on cryptographic schemes are also discussed.

Cross twisted Xate pairing with Barreto-Naehrig curve for multi-pairing technique

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a from G, αG, αdG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r - 1. The infeasibility of DLPwAI assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLP-wAI. This paper shows our experimental results of Cheons algorithm by implementing it with some speeding-up techniques. In fact, we succeeded to solve DLPwAI in a group with 128-bit order in 45 hours with a single PC on an elliptic curve defined over a prime finite field with 256-bit elements which is used in the TinyTate library.

SPIKE: Scalable Peer Intermediaries for Key Establishment in Sensor Networks

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) ⌊log2r⌋. On the other hand, the twisted Ate pairing requires (3/4) ⌊log2r⌋ loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted Ate pairing using Frobenius maps and a small scalar multiplication. The proposal splits the Millers algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Millers algorithm for the proposed twisted Ate pairing is equal to the (1/4) ⌊log2r⌋ attained by the most efficient Ate pairings.