Abstract
In this paper we consider a special type of dual basis for finite fields, GF(2m), where the variants of m are presented in section 2. We introduce our field representing method for efficient field arithmetic(such as field multiplication and field inversion). It reveals a very effective role for both software and hardware(VLSI) implementations, but the aspect of hardware design of its structure is out of this manuscript and so, here, we deal only the case of its software implementation(the efficiency of hardware implementation is appeared in another article submitted to IEEE Transactions on Computers). A brief description of several advantageous characteristics of our method is that (1) the field multiplication in GF(2m) can be constructed only by m + 1 vector rotations and the same amount of vector XOR operations, (2) there is required no additional work load such as basis changing(from standard to dual basis or from dual basis to standard basis as the conventional dual based arithmetic does), (3) the field squaring is only bit-by-bit permutation and it has a good regularity for its implementation, and (4) the field inversion process is available to both cases of its implementation using Fermat’s Theorem and using almost inverse algorithm[14], especially the case of using the almost inverse algorithm has an additional advantage in find- ing(computing) its complete inverse element(i.e., there is required no pre-computed table of the values, x-k, k = 1, 2,…).
| Original language | English |
|---|---|
| Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher | Springer Verlag |
| Pages | 12-28 |
| Number of pages | 17 |
| Volume | 1560 |
| ISBN (Print) | 3540656448, 9783540656449 |
| Publication status | Published - 1999 |
| Event | 2nd International Workshop on Practice and Theory in Public Key Cryptography, PKC 1999 - Kamakura, Japan Duration: 1999 Mar 1 → 1999 Mar 3 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 1560 |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 2nd International Workshop on Practice and Theory in Public Key Cryptography, PKC 1999 |
|---|---|
| Country | Japan |
| City | Kamakura |
| Period | 99/3/1 → 99/3/3 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
A new aspect of dual basis for efficient field arithmetic. / Lee, Chang Hyi; Lim, Jong In.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1560 Springer Verlag, 1999. p. 12-28 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1560).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - A new aspect of dual basis for efficient field arithmetic
AU - Lee, Chang Hyi
AU - Lim, Jong In
PY - 1999
Y1 - 1999
N2 - In this paper we consider a special type of dual basis for finite fields, GF(2m), where the variants of m are presented in section 2. We introduce our field representing method for efficient field arithmetic(such as field multiplication and field inversion). It reveals a very effective role for both software and hardware(VLSI) implementations, but the aspect of hardware design of its structure is out of this manuscript and so, here, we deal only the case of its software implementation(the efficiency of hardware implementation is appeared in another article submitted to IEEE Transactions on Computers). A brief description of several advantageous characteristics of our method is that (1) the field multiplication in GF(2m) can be constructed only by m + 1 vector rotations and the same amount of vector XOR operations, (2) there is required no additional work load such as basis changing(from standard to dual basis or from dual basis to standard basis as the conventional dual based arithmetic does), (3) the field squaring is only bit-by-bit permutation and it has a good regularity for its implementation, and (4) the field inversion process is available to both cases of its implementation using Fermat’s Theorem and using almost inverse algorithm[14], especially the case of using the almost inverse algorithm has an additional advantage in find- ing(computing) its complete inverse element(i.e., there is required no pre-computed table of the values, x-k, k = 1, 2,…).
AB - In this paper we consider a special type of dual basis for finite fields, GF(2m), where the variants of m are presented in section 2. We introduce our field representing method for efficient field arithmetic(such as field multiplication and field inversion). It reveals a very effective role for both software and hardware(VLSI) implementations, but the aspect of hardware design of its structure is out of this manuscript and so, here, we deal only the case of its software implementation(the efficiency of hardware implementation is appeared in another article submitted to IEEE Transactions on Computers). A brief description of several advantageous characteristics of our method is that (1) the field multiplication in GF(2m) can be constructed only by m + 1 vector rotations and the same amount of vector XOR operations, (2) there is required no additional work load such as basis changing(from standard to dual basis or from dual basis to standard basis as the conventional dual based arithmetic does), (3) the field squaring is only bit-by-bit permutation and it has a good regularity for its implementation, and (4) the field inversion process is available to both cases of its implementation using Fermat’s Theorem and using almost inverse algorithm[14], especially the case of using the almost inverse algorithm has an additional advantage in find- ing(computing) its complete inverse element(i.e., there is required no pre-computed table of the values, x-k, k = 1, 2,…).
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UR - http://www.scopus.com/inward/citedby.url?scp=84945290573&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84945290573
SN - 3540656448
SN - 9783540656449
VL - 1560
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 12
EP - 28
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PB - Springer Verlag
ER -