Information: Join today and make your research activities more affordable! Technical workshop participation fees and annual registration fees are available at member rates.
Notice: [Important] Announcement of Changes to Registration Fee Payment and Manuscript Upload Procedures for IEICE Technical Meetings
IEICE Technical Committee Submission System
Conference Paper's Information		 Online Proceedings
[Sign in]
Tech. Rep. Archives
 Go Top Page Go Previous   [Japanese] / [English] 

Paper Abstract and Keywords
Presentation 2026-07-14 15:15
A Sufficient Condition for Zero Reductions in HDF4 Based on Degree-Four Macaulay Matrix Polynomials
Jiei Suto, Kosuke Sakata, Tsuyoshi Takagi (UTokyo) ISEC2026-46 SITE2026-42 BioX2026-69 HWS2026-42 ICSS2026-61 EMM2026-53
Abstract (in Japanese) (See Japanese page) 
(in English) Multivariate public-key cryptography is a type of post-quantum cryptography based on the hardness of solving the MQ problem over finite fields; hence estimating the cost of solving it is important. For Gröbner basis computation for the MQ problem, Sakata and Takagi proposed Hilbert Driven F4 (HDF4), which limits processed S-polynomials in each degree using the number of Gröbner basis polynomials. However, in degree 4, a selected S-polynomial may reduce to 0, namely a zero reduction may occur. In this paper, we give a sufficient condition for zero reductions in degree 4 of HDF4. This condition shows the existence of an S-polynomial that becomes a zero reduction by considering linear subspaces spanned by the degree-4 Macaulay matrix and comparing the set of degree-4 S-polynomials selected by HDF4 with the set of degree-4 Gröbner basis elements. Experiments show that the sufficient condition mainly depends on the number m of equations, and for m=8,...,27, the satisfaction of the sufficient condition coincided with the occurrence of zero reductions.
Keyword (in Japanese) (See Japanese page) 
(in English) post-quantum cryptography / multivariate cryptography / MQ problem / Gröbner basis / HDF4 / zero reduction / /  
Reference Info. IEICE Tech. Rep., vol. 126, no. 107, ISEC2026-46, pp. 224-231, July 2026.
Paper # ISEC2026-46 
Date of Issue 2026-07-06 (ISEC, SITE, BioX, HWS, ICSS, EMM) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF ISEC2026-46 SITE2026-42 BioX2026-69 HWS2026-42 ICSS2026-61 EMM2026-53

Conference Information
Committee BioX HWS ISEC SITE ICSS EMM IPSJ-CSEC IPSJ-SPT 
Conference Date 2026-07-13 - 2026-07-15 
Place (in Japanese) (See Japanese page) 
Place (in English) Sapporo Convention Center 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To ISEC 
Conference Code 2026-07-BioX-HWS-ISEC-SITE-ICSS-EMM-CSEC-SPT-SEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Sufficient Condition for Zero Reductions in HDF4 Based on Degree-Four Macaulay Matrix Polynomials 
Sub Title (in English)  
Keyword(1) post-quantum cryptography  
Keyword(2) multivariate cryptography  
Keyword(3) MQ problem  
Keyword(4) Gröbner basis  
Keyword(5) HDF4  
Keyword(6) zero reduction  
Keyword(7)  
Keyword(8)  
1st Author's Name Jiei Suto  
1st Author's Affiliation The University of Tokyo (UTokyo)
2nd Author's Name Kosuke Sakata  
2nd Author's Affiliation The University of Tokyo (UTokyo)
3rd Author's Name Tsuyoshi Takagi  
3rd Author's Affiliation The University of Tokyo (UTokyo)
4th Author's Name  
4th Author's Affiliation ()
5th Author's Name  
5th Author's Affiliation ()
6th Author's Name  
6th Author's Affiliation ()
7th Author's Name  
7th Author's Affiliation ()
8th Author's Name  
8th Author's Affiliation ()
9th Author's Name  
9th Author's Affiliation ()
10th Author's Name  
10th Author's Affiliation ()
11th Author's Name  
11th Author's Affiliation ()
12th Author's Name  
12th Author's Affiliation ()
13th Author's Name  
13th Author's Affiliation ()
14th Author's Name  
14th Author's Affiliation ()
15th Author's Name  
15th Author's Affiliation ()
16th Author's Name  
16th Author's Affiliation ()
17th Author's Name  
17th Author's Affiliation ()
18th Author's Name  
18th Author's Affiliation ()
19th Author's Name  
19th Author's Affiliation ()
20th Author's Name  
20th Author's Affiliation ()
21st Author's Name  
21st Author's Affiliation ()
22nd Author's Name  
22nd Author's Affiliation ()
23rd Author's Name  
23rd Author's Affiliation ()
24th Author's Name  
24th Author's Affiliation ()
25th Author's Name  
25th Author's Affiliation ()
26th Author's Name / /
26th Author's Affiliation ()
()
27th Author's Name / /
27th Author's Affiliation ()
()
28th Author's Name / /
28th Author's Affiliation ()
()
29th Author's Name / /
29th Author's Affiliation ()
()
30th Author's Name / /
30th Author's Affiliation ()
()
31st Author's Name / /
31st Author's Affiliation ()
()
32nd Author's Name / /
32nd Author's Affiliation ()
()
33rd Author's Name / /
33rd Author's Affiliation ()
()
34th Author's Name / /
34th Author's Affiliation ()
()
35th Author's Name / /
35th Author's Affiliation ()
()
36th Author's Name / /
36th Author's Affiliation ()
()
Speaker Author-1 
Date Time 2026-07-14 15:15:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2026-46, SITE2026-42, BioX2026-69, HWS2026-42, ICSS2026-61, EMM2026-53 
Volume (vol) vol.126 
Number (no) no.107(ISEC), no.108(SITE), no.109(BioX), no.110(HWS), no.111(ICSS), no.112(EMM) 
Page pp.224-231 
#Pages 8 
Date of Issue 2026-07-06 (ISEC, SITE, BioX, HWS, ICSS, EMM) 

[Return to Top Page]

[Return to IEICE Web Page]
The Institute of Electronics, Information and Communication Engineers (IEICE), Japan