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Entity authentication schemes using braid word reduction
 Proc. Internat. Workshop on Coding and Cryptography, 153–164
, 2003
"... Abstract. Artin’s braid groups currently provide a promising background for cryptographical applications, since the first cryptosystems using braids were introduced in [2, 3, 18] (see also [22]). A variety of key agreement protocols based on braids have been described, but few authentication or sign ..."
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Abstract. Artin’s braid groups currently provide a promising background for cryptographical applications, since the first cryptosystems using braids were introduced in [2, 3, 18] (see also [22]). A variety of key agreement protocols based on braids have been described, but few authentication or signature schemes have been proposed so far. We introduce three authentication schemes based on braids, two of them being zeroknowledge interactive proofs of knowledge. Then we discuss their possible implementations, involving normal forms or an alternative braid algorithm, called handle reduction, which can achieve good efficiency under specific requirements. 1.
BraidBased Cryptography
, 2004
"... We survey some of the recently developed cryptographic schemes involving Artin's braid groups, as well as the attacks against these schemes. ..."
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Cited by 19 (1 self)
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We survey some of the recently developed cryptographic schemes involving Artin's braid groups, as well as the attacks against these schemes.
On an algorithm to decide whether a free group is a free factor of another
, 2006
"... We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be m ..."
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Cited by 12 (9 self)
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We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) − rank(H), which often makes a significant change.
New Digital Signature Scheme in Gaussian Monoid
 Informatica, ISSN
"... Abstract. A new digital signature scheme in noncommutative Gaussian monoid is presented. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. Monoid action level ..."
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Cited by 3 (1 self)
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Abstract. A new digital signature scheme in noncommutative Gaussian monoid is presented. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. Monoid action level is defined as monoid element (word) action on module element as an operator. A module is a set of functions (elements) with special properties and could be treated as some generalization of vector space. Signature scheme is based on the oneway functions (OWF) design using: three recognized hard problems in monoid presentation level, one postulated hard problem in monoid action level and one provable hard problem in module action level. For signature creation and verification the word equivalence problem is solved in monoid action level thus avoiding solving it in monoid presentation level. Then the three recognized hard problems in monoid presentation level can be essentially as hard as possible to increase signature security. Thus they do not influence on the word problem complexity and, consequently, on the complexity of signature realization. The investigation of signature scheme security against four kind of attacks is presented. It is shown that the signature has a provable security property with respect to the list of attacks presented here, which are postulated to be complete. Key words: digital signature scheme, oneway function, Gaussian monoid, monoid action problem, conjugator search problem, square root problem, factors ’ search problem.
Secured Directed Digital Signature over NonCommutative Division Semirings and Allocation of Experimental Registration Number Dr. G.S.G.N.Anjaneyulu 1
"... Directed digital signatures are probably the most important and widely used cryptographic primitive enabled by public key technology, and they are building blocks of many modern distributed computer applications. But many existing signatures schemes lie in the intractability of problems closely rela ..."
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Directed digital signatures are probably the most important and widely used cryptographic primitive enabled by public key technology, and they are building blocks of many modern distributed computer applications. But many existing signatures schemes lie in the intractability of problems closely related to the number theory than group theory. In this paper, we present a new directed digital signature scheme based on general noncommutative division semiring. For this, we construct the polynomials as the elements of additive structure of the semiring and take them as the underlying work structure. Then the signature scheme is developed on the multiplicative structure of the division semiring. And also We present one important application ‘Registration Process ’ in different situations in common practice. For this, we use a directed digital signature, to design a scheme such that the scheme provides a registration number to a person or an organization. The registration number can’t be forged and misused and is the strength of the algorithm. The security of the proposed directed signature scheme and registration number is based on the intractability of the Polynomial Symmetrical Decomposition Problem over the given noncommutative division semirings.
Key agreement protocol (KAP) realization in Gaussian group presentation and action levels
 Information Technology and Control
, 2005
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Digital signature scheme based on action of infinite ring. Information Technoconstructed on the basis of CSP but nevertheless the logy and Control
 ISSN 1392124X
, 2004
"... Abstract. An original digital signature scheme based on action of infinite ring on module is presented. It is assumed that the ring contains an infinite multiplicative monoid. The ring action is defined as monoid elements's action on the module element as an operator. The signature scheme is ba ..."
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Cited by 1 (1 self)
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Abstract. An original digital signature scheme based on action of infinite ring on module is presented. It is assumed that the ring contains an infinite multiplicative monoid. The ring action is defined as monoid elements's action on the module element as an operator. The signature scheme is based on particularly designed one–way functions (OWFs), using a postulated hard problem in monoid action level. The investigation of signature scheme security against three kinds of attacks is presented. Referencing to the postulated OWFs, the proposed signature scheme has provable security property.
OPEN JOURNAL OF INFORMATION SECURITY AND APPLICATIONS ZeroKnowledge Authentication Schemes Using QuasiPolynomials over NonCommutative Groups
"... A zeroknowledge authentication scheme is a type of authentication scheme, which gives no knowledge beyond the authenticity identifying an entity and is probabilistic than deterministic authentication scheme. This paper proposes DiffieHellman and FiatShamir like zeroknowledge authentication schem ..."
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A zeroknowledge authentication scheme is a type of authentication scheme, which gives no knowledge beyond the authenticity identifying an entity and is probabilistic than deterministic authentication scheme. This paper proposes DiffieHellman and FiatShamir like zeroknowledge authentication schemes on general noncommutative groups. The key idea of our proposal is that for a given noncommutative group one can define quasipolynomials and takes them as underlying work structure. In doing so,one can implement the schemes. The security of the proposed schemes is based on the intractability of the quasipolynomial symmetrical decomposition problem over the given noncommutative group. Keywords:
Contemporary Mathematics Using shifted conjugacy in braidbased cryptography
, 2006
"... Abstract. Conjugacy is not the only possible primitive for designing braidbased protocols. To illustrate this principle, we describe a Fiat–Shamirstyle authentication protocol that be can be implemented using any binary operation that satisfies the left selfdistributive law. Conjugation is an exam ..."
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Abstract. Conjugacy is not the only possible primitive for designing braidbased protocols. To illustrate this principle, we describe a Fiat–Shamirstyle authentication protocol that be can be implemented using any binary operation that satisfies the left selfdistributive law. Conjugation is an example of such an operation, but there are other examples, in particular the shifted conjugation on Artin’s braid group B∞, and the finite Laver tables. In both cases, the underlying structures have a high combinatorial complexity, and they lead to difficult problems. Most of the braidbased cryptographic schemes proposed so far [1, 18, 3] rely on the supposed complexity of the conjugation operation in Artin’s braid groups. In this note, we would like to stress the fact that conjugation is by far not the only possible primitive operation for designing braidbased protocols. To illustrate this general idea on a concrete example, we shall discuss an authentication scheme directly reminiscent of the Fiat–Shamir scheme, and a variant of some scheme considered in [20] in the case of braids. We show that such a