TY - JOUR
T1 - Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields
AU - Adj, Gora
AU - Canales-Martínez, Isaac
AU - Cruz-Cortés, Nareli
AU - Menezes, Alfred
AU - Oliveira, Thomaz
AU - Rivera-Zamarripa, Luis
AU - Rodríguez-Henríquez, Francisco
N1 - Publisher Copyright:
© 2018 AIMS.
PY - 2018/11
Y1 - 2018/11
N2 - Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasi-polynomial algorithm. In this paper, we report on our successful computation of discrete logarithms in the cryptographically-interesting characteristic-three finite field F 36·509 using these new algorithms; prior to 2013, it was believed that this field enjoyed a security level of 128 bits. We also show that a recent idea of Guillevic can be used to compute discrete logarithms in the cryptographically-interesting finite field F 36·709 using essentially the same resources as we expended on the F 36·509 computation. Finally, we argue that discrete logarithms in the finite field F 36·1429 can feasibly be computed today; this is significant because this cryptographically-interesting field was previously believed to enjoy a security level of 192 bits.
AB - Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasi-polynomial algorithm. In this paper, we report on our successful computation of discrete logarithms in the cryptographically-interesting characteristic-three finite field F 36·509 using these new algorithms; prior to 2013, it was believed that this field enjoyed a security level of 128 bits. We also show that a recent idea of Guillevic can be used to compute discrete logarithms in the cryptographically-interesting finite field F 36·709 using essentially the same resources as we expended on the F 36·509 computation. Finally, we argue that discrete logarithms in the finite field F 36·1429 can feasibly be computed today; this is significant because this cryptographically-interesting field was previously believed to enjoy a security level of 192 bits.
KW - Discrete logarithm problem
KW - Finite fields
KW - Pairing-based cryptography
UR - http://www.scopus.com/inward/record.url?scp=85063235503&partnerID=8YFLogxK
U2 - 10.3934/amc.2018044
DO - 10.3934/amc.2018044
M3 - Artículo
AN - SCOPUS:85063235503
SN - 1930-5346
VL - 12
SP - 741
EP - 759
JO - Advances in Mathematics of Communications
JF - Advances in Mathematics of Communications
IS - 4
ER -