Cryptanalysis of a GL(r,Zn)-Based Public Key System
Summary :
Keith Salvin presented a key exchange protocol using matrices in the general linear group, GL(r,Zn), where n is the product of two distinct large primes. The system is fully specified in the US patent number 7346162 issued in 2008. In the patent claims, it is argued that the best way to break this system is to factor n. Furthermore, for efficiency reasons, it is suggested to use r=2. In this letter, we show that this cryptosystem can be easily broken by solving a set of consistent homogeneous r2 linear equations in 2r unknowns over Zn.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.4 pp.829-831
- Publication Date
- 2012/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E95.A.829
- Type of Manuscript
- LETTER
- Category
- Cryptography and Information Security
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Keyword
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Abdel Alim KAMAL, Amr YOUSSEF, "Cryptanalysis of a GL(r,Zn)-Based Public Key System" in IEICE TRANSACTIONS on Fundamentals,
vol. E95-A, no. 4, pp. 829-831, April 2012, doi: 10.1587/transfun.E95.A.829.
Abstract: Keith Salvin presented a key exchange protocol using matrices in the general linear group, GL(r,Zn), where n is the product of two distinct large primes. The system is fully specified in the US patent number 7346162 issued in 2008. In the patent claims, it is argued that the best way to break this system is to factor n. Furthermore, for efficiency reasons, it is suggested to use r=2. In this letter, we show that this cryptosystem can be easily broken by solving a set of consistent homogeneous r2 linear equations in 2r unknowns over Zn.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.829/_p
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@ARTICLE{e95-a_4_829,
author={Abdel Alim KAMAL, Amr YOUSSEF, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cryptanalysis of a GL(r,Zn)-Based Public Key System},
year={2012},
volume={E95-A},
number={4},
pages={829-831},
abstract={Keith Salvin presented a key exchange protocol using matrices in the general linear group, GL(r,Zn), where n is the product of two distinct large primes. The system is fully specified in the US patent number 7346162 issued in 2008. In the patent claims, it is argued that the best way to break this system is to factor n. Furthermore, for efficiency reasons, it is suggested to use r=2. In this letter, we show that this cryptosystem can be easily broken by solving a set of consistent homogeneous r2 linear equations in 2r unknowns over Zn.},
keywords={},
doi={10.1587/transfun.E95.A.829},
ISSN={1745-1337},
month={April},}
Copy
TY - JOUR
TI - Cryptanalysis of a GL(r,Zn)-Based Public Key System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 829
EP - 831
AU - Abdel Alim KAMAL
AU - Amr YOUSSEF
PY - 2012
DO - 10.1587/transfun.E95.A.829
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2012
AB - Keith Salvin presented a key exchange protocol using matrices in the general linear group, GL(r,Zn), where n is the product of two distinct large primes. The system is fully specified in the US patent number 7346162 issued in 2008. In the patent claims, it is argued that the best way to break this system is to factor n. Furthermore, for efficiency reasons, it is suggested to use r=2. In this letter, we show that this cryptosystem can be easily broken by solving a set of consistent homogeneous r2 linear equations in 2r unknowns over Zn.
ER -
English
