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New Public-Key Cryptosystem Using Braid Groups [chapter]

Ki Hyoung Ko, Sang Jin Lee, Jung Hee Cheon, Jae Woo Han, Ju-sung Kang, Choonsik Park
2000 Lecture Notes in Computer Science  
The other is to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in the braid groups.  ...  The foundation of our systems is quite different from widely used cryptosystems based on number theory, but there are some similarities in design.  ...  The first two authors also wish to thank Joan Birman for her kind introduction of the braid theory and her continuing encouragement.  ... 
doi:10.1007/3-540-44598-6_10 fatcat:xikagrbu5ffdbavgvhr7xdk56q

Page 7006 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
cryptosystem using braid groups.  ...  The other aim is to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in the braid groups.  ... 

Provably Secure Integration Cryptosystem on Non-Commutative Group [article]

Xiaoming Chen, Weiqing You
2018 arXiv   pre-print
The other is to propose a new public key cryptosystem over braid group which is secure against adaptive chosen-ciphertext-attack(CCA2).  ...  This paper focuses on the provable security research of cryptosystem over braid group, which consists of two aspects: One, we proved that the Ko's cryptosystem based on braid group is secure against chosen-plaintext-attack  ...  Provably Secure Integration Cryptosystem on Non-Commutative Group  ... 
arXiv:1806.03075v2 fatcat:ikku5h2kwvamzeuk2mq6dg2mi4

Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem

Delaram Kahrobaei, Michael Anshel
2009 Groups - Complexity - Cryptology  
A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable / polycyclic group is suggested.  ...  In 2004, Eick and Kahrobaei [12] proposed a new cryptosystem based on polycyclic groups. In 2005 Baumslag, Fine and Xu proposed public key cryptosystem using the modular group [3] , [4] .  ...  Non-Commutative public key cryptosystem using Conjugacy The following is the public key cryptosystem problem proposed by Kahrobaei and Khan [20] .  ... 
doi:10.1515/gcc.2009.217 fatcat:isdna5jto5c5pc7pmnzkdc7sym

Length-Based Attacks for Certain Group Based Encryption Rewriting Systems [article]

James Hughes, Allen Tannenbaum
2003 arXiv   pre-print
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld  ...  Such canonical representatives are known to exist for the braid group.  ...  We should first note however that the use of the word and conjugacy problems for public-key cryptosystems is not new. An early reference is [26] .  ... 
arXiv:cs/0306032v1 fatcat:x6j7ch3o7vcjte7dunngqf6iiq

Decision and Search in Non-abelian Cramer Shoup Public Key Cryptosystem [article]

Michael Anshel, Delaram Kahrobaei
2013 arXiv   pre-print
A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable/polycyclic group is suggested.  ...  In 2004, Eick and Kahrobaei [12] proposed a new cryptosystem based on polycyclic groups. In 2005 Baumslag, Fine and Xu proposed public key cryptosystem using the modular group [3] , [4] .  ...  And finally, Birget et al. proposed a new public-key cryptosystem which is based on finitely presented groups with hard word problem. In 1999, Anshel et al.  ... 
arXiv:1309.4519v1 fatcat:avb4yo37lrbwzgzzkjifvuc5bq

Braid Group Cryptography [article]

David Garber
2008 arXiv   pre-print
In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed.  ...  This survey includes: Basic facts on braid groups and on the Garside normal form of its elements, some known algorithms for solving the word problem in the braid group, the major public-key cryptosystems  ...  Acknowledgements First, I wish to thank the organizers of the PRIMA school and conference on Braids which took place at Singapore in June 2007, Jon Berrick and Fred  ... 
arXiv:0711.3941v2 fatcat:etc5sbsvyvemplcyme2jeqsije

Conjugate adjoining problem in braid groups and new design of braid-based signatures

LiCheng Wang, LiHua Wang, ZhenFu Cao, YiXian Yang, XinXin Niu
2010 Science China Information Sciences  
The development of quantum computation casts serious threats to the securities of most existing public-key cryptosystems.  ...  The key sizes in braid-based schemes are considerably large-about 2K bits in the case of secret keys and 12K bits in the case of public keys.  ...  Introduction Today, most public-key cryptosystems that remain unbroken are based on the perceived difficulty of solving certain problems in particular large finite (abelian) groups.  ... 
doi:10.1007/s11432-010-0046-4 fatcat:5mtzgtp32rcdzfcmh7cedyrtbq

Group theory in cryptography [article]

Simon R. Blackburn, Carlos Cid, Ciaran Mullan
2010 arXiv   pre-print
This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory.  ...  The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.  ...  Thus it seems that a significant new idea in this area is needed to construct a secure public key cryptosystem from logarithmic signatures.  ... 
arXiv:0906.5545v2 fatcat:hos33mtpa5fshh2rd6nkoyj4tq

Towards generating secure keys for braid cryptography

Ki Hyoung Ko, Jang Won Lee, Tony Thomas
2007 Designs, Codes and Cryptography  
Braid cryptosystem was proposed in CRYPTO 2000 as an alternate public-key cryptosystem. The security of this system is based upon the conjugacy problem in braid groups.  ...  Since then, there have been several attempts to break the braid cryptosystem by solving the conjugacy problem in braid groups.  ...  The left-canonical form is used as the final normal form for the shared key. 2.4.3. Braid Public-key Cryptosystem. In 2000 Ko et al.  ... 
doi:10.1007/s10623-007-9123-0 fatcat:aijbus7j7jcadnortffo4wa5ca

Aspects of Nonabelian Group Based Cryptography: A Survey and Open Problems [article]

Benjamin Fine, Maggie Habeeb, Delaram Kahrobaei, Gerhard Rosenberger
2011 arXiv   pre-print
This was initiated by two public key protocols that used the braid groups, one by Ko, Lee et.al.and one by Anshel, Anshel and Goldfeld.  ...  Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on  ...  However a public key free group cryptosystem using a free group representation in the Modular group was developed by Baumslag, Fine and Xu [BFX 1 2] .  ... 
arXiv:1103.4093v2 fatcat:7yqcyw2yv5dd3ghgai54bxuzx4

A New Key Exchange Protocol Based on Infinite Non-Abelian Groups

Jing Zhang, Ya-Juan Yang, Yi-Peng Li, Xingsi Xue
2022 Security and Communication Networks  
In order to resist quantum attacks, a key exchange protocol based on infinite non-abelian groups is proposed in this paper.  ...  Finally, we analyzed the computational complexity and bit complexity when the protocol being implemented on braid groups, and furthermore, the complexity data confirm the feasibility of establishing the  ...  proposed a new idea that infinite non-abelian group and semigroup can be used in public key cryptography [1] . e main problem of key exchange protocol on infinite non-abelian (semi) group is to hide some  ... 
doi:10.1155/2022/7942353 fatcat:hxflvuf5lzdflbmyiczuxkv2by

Encryption Scheme using Non-Abelian Group based on Conjugacy Search Problem

2020 ASM Science Journal  
Non-abelian group public key cryptography is a relatively new and exciting research field.  ...  As a result, we choose to work over a non-abelian group called Miller group in which its automorphism group is abelian.  ...  There are several groupbased public key protocols used the hardness of this problem in some particular groups for instance braid groups, refer (Hasapis et al., 2015; Ko et al., 2000; Myasnikov et al.,  ... 
doi:10.32802/asmscj.2020.sm26(5.11) fatcat:b2xocloxubb33f7ph3q7auwgwu

Towards a Uniform Description of Several Group Based Cryptographic Primitives

María Isabel González Vasco, Consuelo Martínez, Rainer Steinwandt
2004 Designs, Codes and Cryptography  
The public key cryptosystems M ST 1 and M ST 2 make use of certain kinds of factorizations of finite groups.  ...  In particular, a generalization of M ST 2 can be regarded as a unifying framework for several suggested cryptosystems including the ElGamal public key system, a public key system based on braid groups  ...  of such a generalized M ST 2 scheme: the ElGamal public key system [2] , the braid group based public key system from [4] , and the MOR cryptosystem from [7, 8] .  ... 
doi:10.1023/b:desi.0000036247.38461.c9 fatcat:gu2fhuhtirfulopkokeblpc32q

Noncommutative Lightweight Signcryption for Wireless Sensor Networks

Lize Gu, Yun Pan, Mianxiong Dong, Kaoru Ota
2013 International Journal of Distributed Sensor Networks  
In this paper, we at first propose a braid-based signcryption scheme and then develop a key establishment protocol for wireless sensor networks.  ...  Key management techniques for secure wireless-sensor-networks-based applications must minimally incorporate confidentiality, authenticity, integrity, scalability, and flexibility.  ...  [24] proposed several public-key cryptosystems based on conjugacy-based left self-distributive systems.  ... 
doi:10.1155/2013/818917 fatcat:gzlglbgue5eahkk7336gtxljrm
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