Abstract
We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 b + c+ x b + c+ x b+ x c+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F 2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.
| Original language | English |
|---|---|
| Pages (from-to) | 359–373 |
| Number of pages | 15 |
| Journal | Journal of Cryptographic Engineering |
| Volume | 9 |
| Issue number | 4 |
| Early online date | 9 Nov 2018 |
| DOIs | |
| Publication status | Published - 1 Nov 2019 |
Fingerprint
Keywords
- Finite fields
- Irreducible pentanomials
- Modular reduction
- Polynomial multiplication
Cite this
}
A new class of irreducible pentanomials for polynomial-based multipliers in binary fields. / Banegas, Gustavo (Corresponding author); Custódio, Ricardo; Panario, Daniel.
In: Journal of Cryptographic Engineering, Vol. 9, No. 4, 01.11.2019, p. 359–373.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - A new class of irreducible pentanomials for polynomial-based multipliers in binary fields
AU - Banegas, Gustavo
AU - Custódio, Ricardo
AU - Panario, Daniel
PY - 2019/11/1
Y1 - 2019/11/1
N2 - We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 b + c+ x b + c+ x b+ x c+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F 2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.
AB - We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 b + c+ x b + c+ x b+ x c+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F 2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.
KW - Finite fields
KW - Irreducible pentanomials
KW - Modular reduction
KW - Polynomial multiplication
UR - http://www.scopus.com/inward/record.url?scp=85073577324&partnerID=8YFLogxK
U2 - 10.1007/s13389-018-0197-6
DO - 10.1007/s13389-018-0197-6
M3 - Article
VL - 9
SP - 359
EP - 373
JO - Journal of Cryptographic Engineering
JF - Journal of Cryptographic Engineering
SN - 2190-8508
IS - 4
ER -