The multi-variable modular polynomial and its applications to cryptography

Tsuyoshi Takagi; Shozo Naito

doi:10.1007/bfb0009515

The multi-variable modular polynomial and its applications to cryptography

Tsuyoshi Takagi, Shozo Naito

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Citations (Scopus)

Abstract

We prove the extension of the Håstad algorithm to the multi-variable modular polynomial. Although the Håstad attack is one of the strongest known attacks on RSA-type cryptosystems, the original Håstad attack is generally not applicable to multi-variable cryptosystems, where the plain text space (the encryption domain) is multi-variable. As an application of our extension, we attack RSA-type cryptosystems over elliptic curves and show the critical number of encrypted texts.

Original language	English
Title of host publication	Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings
Editors	Tetsuo Asano, Yoshihide Igarashi, Hiroshi Nagamochi, Satoru Miyano, Subhash Suri
Publisher	Springer Verlag
Pages	386-396
Number of pages	11
ISBN (Print)	3540620486, 9783540620488
DOIs	https://doi.org/10.1007/bfb0009515
Publication status	Published - Jan 1 1996
Event	7th International Symposium on Algorithms and Computation, ISAAC 1996 - Osaka, Japan Duration: Dec 16 1996 → Dec 18 1996

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1178
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th International Symposium on Algorithms and Computation, ISAAC 1996
Country	Japan
City	Osaka
Period	12/16/96 → 12/18/96

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/bfb0009515

Fingerprint Dive into the research topics of 'The multi-variable modular polynomial and its applications to cryptography'. Together they form a unique fingerprint.

Cite this

Takagi, T., & Naito, S. (1996). The multi-variable modular polynomial and its applications to cryptography. In T. Asano, Y. Igarashi, H. Nagamochi, S. Miyano, & S. Suri (Eds.), Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings (pp. 386-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1178). Springer Verlag. https://doi.org/10.1007/bfb0009515

The multi-variable modular polynomial and its applications to cryptography. / Takagi, Tsuyoshi; Naito, Shozo.

Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings. ed. / Tetsuo Asano; Yoshihide Igarashi; Hiroshi Nagamochi; Satoru Miyano; Subhash Suri. Springer Verlag, 1996. p. 386-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1178).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Takagi, T & Naito, S 1996, The multi-variable modular polynomial and its applications to cryptography. in T Asano, Y Igarashi, H Nagamochi, S Miyano & S Suri (eds), Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1178, Springer Verlag, pp. 386-396, 7th International Symposium on Algorithms and Computation, ISAAC 1996, Osaka, Japan, 12/16/96. https://doi.org/10.1007/bfb0009515

Takagi T, Naito S. The multi-variable modular polynomial and its applications to cryptography. In Asano T, Igarashi Y, Nagamochi H, Miyano S, Suri S, editors, Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings. Springer Verlag. 1996. p. 386-396. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/bfb0009515

Takagi, Tsuyoshi ; Naito, Shozo. / The multi-variable modular polynomial and its applications to cryptography. Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings. editor / Tetsuo Asano ; Yoshihide Igarashi ; Hiroshi Nagamochi ; Satoru Miyano ; Subhash Suri. Springer Verlag, 1996. pp. 386-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{1933ae96b0d8446ebec66e996de96cb7,

title = "The multi-variable modular polynomial and its applications to cryptography",

abstract = "We prove the extension of the H{\aa}stad algorithm to the multi-variable modular polynomial. Although the H{\aa}stad attack is one of the strongest known attacks on RSA-type cryptosystems, the original H{\aa}stad attack is generally not applicable to multi-variable cryptosystems, where the plain text space (the encryption domain) is multi-variable. As an application of our extension, we attack RSA-type cryptosystems over elliptic curves and show the critical number of encrypted texts.",

author = "Tsuyoshi Takagi and Shozo Naito",

year = "1996",

month = jan,

day = "1",

doi = "10.1007/bfb0009515",

language = "English",

isbn = "3540620486",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "386--396",

editor = "Tetsuo Asano and Yoshihide Igarashi and Hiroshi Nagamochi and Satoru Miyano and Subhash Suri",

booktitle = "Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings",

address = "Germany",

note = "7th International Symposium on Algorithms and Computation, ISAAC 1996 ; Conference date: 16-12-1996 Through 18-12-1996",

}

TY - GEN

T1 - The multi-variable modular polynomial and its applications to cryptography

AU - Takagi, Tsuyoshi

AU - Naito, Shozo

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We prove the extension of the Håstad algorithm to the multi-variable modular polynomial. Although the Håstad attack is one of the strongest known attacks on RSA-type cryptosystems, the original Håstad attack is generally not applicable to multi-variable cryptosystems, where the plain text space (the encryption domain) is multi-variable. As an application of our extension, we attack RSA-type cryptosystems over elliptic curves and show the critical number of encrypted texts.

AB - We prove the extension of the Håstad algorithm to the multi-variable modular polynomial. Although the Håstad attack is one of the strongest known attacks on RSA-type cryptosystems, the original Håstad attack is generally not applicable to multi-variable cryptosystems, where the plain text space (the encryption domain) is multi-variable. As an application of our extension, we attack RSA-type cryptosystems over elliptic curves and show the critical number of encrypted texts.

UR - http://www.scopus.com/inward/record.url?scp=84990218567&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990218567&partnerID=8YFLogxK

U2 - 10.1007/bfb0009515

DO - 10.1007/bfb0009515

M3 - Conference contribution

AN - SCOPUS:84990218567

SN - 3540620486

SN - 9783540620488

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 386

EP - 396

BT - Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings

A2 - Asano, Tetsuo

A2 - Igarashi, Yoshihide

A2 - Nagamochi, Hiroshi

A2 - Miyano, Satoru

A2 - Suri, Subhash

PB - Springer Verlag

T2 - 7th International Symposium on Algorithms and Computation, ISAAC 1996

Y2 - 16 December 1996 through 18 December 1996

ER -

The multi-variable modular polynomial and its applications to cryptography

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this