A public key cryptosystem based on the word problem
Proceedings of CRYPTO 84 on Advances in cryptology
Some public key crypto-functions as intractable as factorization
Proceedings of CRYPTO 84 on Advances in cryptology
Proceedings of CRYPTO 84 on Advances in cryptology
Enumerative combinatorics
A key distribution system equivalent to factoring
Journal of Cryptology
A public key cryptosystem based on Lyndon words
Information Processing Letters
The set of minimal braids is Co-NP-complete
Journal of Algorithms
The complexity of Grigorchuk groups with application to cryptography
Theoretical Computer Science
Algebraic aspects of cryptography
Algebraic aspects of cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Word Processing in Groups
New Public-Key Schemes Based on Elliptic Curves over the Ring Zn
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Chor-Rivest Cryptosystem
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
IFIP/Sec '93 Proceedings of the IFIP TC11, Ninth International Conference on Information Security: Computer Security
On the Security of ElGamal Based Encryption
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
New Key Agreement Protocols in Braid Group Cryptography
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
New Public Key Cryptosystem Using Finite Non Abelian Groups
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Pseudorandomness from Braid Groups
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Potential Weaknesses of the Commutator Key Agreement Protocol Based on Braid Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Cryptanalysis of a Pseudorandom Generator Based on Braid Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
An Efficient Implementation of Braid Groups
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A Practical Attack on Some Braid Group Based Cryptographic Primitives
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Security Analysis of the MOR Cryptosystem
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
On the cycling operation in braid groups
Discrete Applied Mathematics
A Non-abelian Group Based on Block Upper Triangular Matrices with Cryptographic Applications
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A new hard problem over non-commutative finite groups for cryptographic protocols
MMM-ACNS'10 Proceedings of the 5th international conference on Mathematical methods, models and architectures for computer network security
A Novel Combinatorial Public Key Cryptosystem
Informatica
Cryptanalysis of cryptosystems based on non-commutative skew polynomials
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
New constructions of public-key encryption schemes from conjugacy search problems
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Towards provably secure group key agreement building on group theory
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
Reduction of conjugacy problem in braid groups, using two garside structures
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Diophantine approximation attack on a fast public key cryptosystem
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
Thompson's group and public key cryptography
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
A new cramer-shoup like methodology for group based provably secure encryption schemes
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
A practical attack on a braid group based cryptographic protocol
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Reducing the key size of rainbow using non-commutative rings
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
| Hi-index | 0.00 |
The braid groups are infinite non-commutative groups naturally arising from geometric braids. The aim of this article is twofold. One is to show that the braid groups can serve as a good source to enrich cryptography. The feature that makes the braid groups useful to cryptography includes the followings: (i) The word problem is solved via a fast algorithm which computes the canonical form which can be efficiently manipulated by computers. (ii) The group operations can be performed efficiently. (iii) The braid groups have many mathematically hard problems that can be utilized to design cryptographic primitives. 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 efficiency of our systems is demonstrated by their speed and information rate. The security of our systems is based on topological, combinatorial and group-theoretical problems that are intractible according to our current mathematical knowledge. The foundation of our systems is quite different from widely used cryptosystems based on number theory, but there are some similarities in design.