Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Elliptic curves in cryptography
Elliptic curves in cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Satoh's algorithm in characteristic 2
Mathematics of Computation
A Memory Efficient Version of Satoh's Algorithm
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Computing l-Isogenies Using the p-Torsion
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast computation of canonical lifts of elliptic curves and its application to point counting
Finite Fields and Their Applications
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Fast arithmetic in unramified p-adic fields
Finite Fields and Their Applications
| Hi-index | 0.00 |
In this paper we present an improved algorithm for counting points on elliptic curves over finite fields. It is mainly based on Satoh-Skjernaa-Taguchi algorithm [SST01], and uses a Gaussian Normal Basis (GNB) of small type t 驴 4. In practice, about 42% (36% for prime N) of fields in cryptographic context (i.e., for p = 2 and 160 N pN to ZpN in a natural way. From the specific properties of GNBs, efficient multiplication and the Frobenius substitution are available. Thus a fast norm computation algorithm is derived, which runs in O(N2碌 log N) with O(N2) space, where the time complexity of multiplying two n-bit objects is O(n碌). As a result, for all small characteristic p, we reduced the time complexity of the SST-algorithm from O(N2碌+0.5) to O(N2碌+ 1/碌+1) and the space complexity still fits in O(N2). Our approach is expected to be applicable to the AGM since the exhibited improvement is not restricted to only [SST01].