Efficient subgroup exponentiation in quadratic and sixth degree
  extensions

M Stam; AK Lenstra

Efficient subgroup exponentiation in quadratic and sixth degree extensions

M Stam, AK Lenstra

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

Abstract

This paper describes several speedups for computation in the order $p+1$ subgroup of $\GaF{p^2}^*$ and the order $p^2-p+1$ subgroup of~$\GaF{p^6}^*$. These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with $p\equiv3\bmod 4$.

Translated title of the contribution	Efficient subgroup exponentiation in quadratic and sixth degree extensions
Original language	English
Title of host publication	Cryptographic Hardware and Embedded Systems - CHES 2002
Publisher	Springer Berlin Heidelberg
Pages	318 - 332
Number of pages	14
Volume	2523
ISBN (Print)	3540004092
Publication status	Published - 2002

Bibliographical note

Conference Proceedings/Title of Journal: Cryptographic Hardware and Embedded Systems - CHES 2002, 4th
International Workshop, Redwood Shores, CA, USA, August 13-15,
2002, Revised Papers

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Cite this

@inproceedings{50cce07ab5d5485986b52eb2cd577901,

title = "Efficient subgroup exponentiation in quadratic and sixth degree extensions",

abstract = " This paper describes several speedups for computation in the order \$p+1\$ subgroup of \$\textbackslash{}GaF\{p\textasciicircum{}2\}\textasciicircum{}*\$ and the order \$p\textasciicircum{}2-p+1\$ subgroup of\textasciitilde{}\$\textbackslash{}GaF\{p\textasciicircum{}6\}\textasciicircum{}*\$. These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with \$p\textbackslash{}equiv3\textbackslash{}bmod 4\$. ",

author = "M Stam and AK Lenstra",

note = "Conference Proceedings/Title of Journal: Cryptographic Hardware and Embedded Systems - CHES 2002, 4th International Workshop, Redwood Shores, CA, USA, August 13-15, 2002, Revised Papers",

year = "2002",

language = "English",

isbn = "3540004092",

volume = "2523",

pages = "318 -- 332",

booktitle = "Cryptographic Hardware and Embedded Systems - CHES 2002",

publisher = "Springer Berlin Heidelberg",

address = "Germany",

}

TY - GEN

T1 - Efficient subgroup exponentiation in quadratic and sixth degree extensions

AU - Stam, M

AU - Lenstra, AK

N1 - Conference Proceedings/Title of Journal: Cryptographic Hardware and Embedded Systems - CHES 2002, 4th International Workshop, Redwood Shores, CA, USA, August 13-15, 2002, Revised Papers

PY - 2002

Y1 - 2002

N2 - This paper describes several speedups for computation in the order $p+1$ subgroup of $\GaF{p^2}^*$ and the order $p^2-p+1$ subgroup of~$\GaF{p^6}^*$. These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with $p\equiv3\bmod 4$.

AB - This paper describes several speedups for computation in the order $p+1$ subgroup of $\GaF{p^2}^*$ and the order $p^2-p+1$ subgroup of~$\GaF{p^6}^*$. These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with $p\equiv3\bmod 4$.

M3 - Conference Contribution (Conference Proceeding)

SN - 3540004092

VL - 2523

SP - 318

EP - 332

BT - Cryptographic Hardware and Embedded Systems - CHES 2002

PB - Springer Berlin Heidelberg