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New Approaches to Designing Public Key Cryptosystems Using OneWay Functions and TrapDoors in Finite Groups
 Journal of Cryptology
"... A symmetric key cryptosystem based on logarithmic signatures for nite permutation groups was described by the rst author in [6], and its algebraic properties were studied in [7]. In this paper we describe two possible approaches to the construction of new public key cryptosystems with message spa ..."
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Cited by 24 (3 self)
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A symmetric key cryptosystem based on logarithmic signatures for nite permutation groups was described by the rst author in [6], and its algebraic properties were studied in [7]. In this paper we describe two possible approaches to the construction of new public key cryptosystems with message space a large nite group G, using logarithmic signatures and their generalizations. The rst approach relies on the fact that permutations of the message space G induced by transversal logarithmic signatures almost always generate the full symmetric group SG on the message space. The second approach could potentially lead to new ElGamal  like systems based on trapdoor, oneway functions induced Research supported in part by National Science Foundation grant CCR9610138 y Research supported in part by NSERC grants IRC #21643196 and RGPIN # 20311498. 1 by logarithmic signaturelike objects we call meshes, which are uniform covers for G. Key words. Trapdoor oneway functions...
Algorithms for Matrix Groups and the Tits Alternative
 Proc. 36th IEEE FOCS
, 1999
"... l over the generators grows as c l for some constant c>1 depending on G. For groups with abelian subgroups of finite index, we obtain a Las Vegas algorithm for several basic computational tasks, including membership testing and computing a presentation. This generalizes recent work of Beals ..."
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Cited by 11 (2 self)
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l over the generators grows as c l for some constant c>1 depending on G. For groups with abelian subgroups of finite index, we obtain a Las Vegas algorithm for several basic computational tasks, including membership testing and computing a presentation. This generalizes recent work of Beals and Babai, who give a Las Vegas algorithm for the case of finite groups, as well as recent work of Babai, Beals, Cai, Ivanyos, and Luks, who give a deterministic algorithm for the case of abelian groups. # 1999 Academic Press Article ID jcss.1998.1614, available online at http:##www.idealibrary.com on 260 00220000#99 #30.00 Copyright # 1999 by Academic Press All rights of reproduction in any form reserved. * Research conducted while visiting IAS and DIMACS and supported in part by an NSF Mathematical Sciences
Compression independent object encryption for ensuring privacy in video surveillance
 IEEE International Conference on Multimedia and Expo
, 2008
"... One of the main concerns of the wide use of video surveillance is the loss of individual privacy. Individuals who are not suspects need not be identified on camera recordings. Mechanisms that protect the identity while ensuring legitimate security needs are necessary. Selectively encrypting objects ..."
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Cited by 10 (1 self)
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One of the main concerns of the wide use of video surveillance is the loss of individual privacy. Individuals who are not suspects need not be identified on camera recordings. Mechanisms that protect the identity while ensuring legitimate security needs are necessary. Selectively encrypting objects that reveal identity (e.g., faces or vehicle tags) is necessary to preserve individuals ’ right to privacy. This paper presents a compression algorithm independent solution that provides privacy in video surveillance applications. The proposed approach is based on the use of permutation based encryption to hide identity revealing features. The permutation based encryption tolerates lossy compression and allows decryption at a later time. The use of permutation based encryption makes the proposed solution independent of the compression algorithms used. The paper presents the performance of the system when using H.264 video encoding. Index Terms — video surveillance, compression, privacy, identity, encryption
SECRETAND PUBLICKEY CRYPTOSYSTEMS FROM GROUP FACTORIZATIONS
, 2002
"... Many known cryptosystems, symmetric or asymmetric, have been based on properties of large abelian groups. Here we discuss cryptosystems based on nonabelian, in fact nonsolvable groups. A symmetric key cryptosystem based on logarithmic signatures for finite permutation groups was proposed by the ..."
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Cited by 7 (0 self)
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Many known cryptosystems, symmetric or asymmetric, have been based on properties of large abelian groups. Here we discuss cryptosystems based on nonabelian, in fact nonsolvable groups. A symmetric key cryptosystem based on logarithmic signatures for finite permutation groups was proposed by the author in [S. S. Magliveras: A cryptosystem from logarithmic signatures of finite
A Public Key Cryptosystem Based on Nonabelian Finite Groups
 Journal of Cryptology
"... We present a new approach to designing publickey cryptosystems, based on covers and logarithmic signatures of nonabelian nite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2groups for which we are able to prove the security o ..."
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We present a new approach to designing publickey cryptosystems, based on covers and logarithmic signatures of nonabelian nite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2groups for which we are able to prove the security of the system under conceivable attacks. The proofs provide lower bounds of the workload needed by an adversary to launch such an attack, and provide strong security evidence for the system. The system is scallable, and the proposed underlying group, represented as a matrix group, aords signicant space and time eciency. Key words. Publickey cryptosystem, logarithmic signature, uniform cover, trapdoor oneway function, Suzuki 2group. 1
On Minimal Length Factorizations of Finite Groups
, 2003
"... Logarithmic signatures are a special type of group factorizations, introduced as basic components of certain cryptographic keys. Thus, short logarithmic signatures are of special interest. We deal with the question of nding logarithmic signatures of minimal length in nite groups. In particular ..."
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Cited by 4 (0 self)
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Logarithmic signatures are a special type of group factorizations, introduced as basic components of certain cryptographic keys. Thus, short logarithmic signatures are of special interest. We deal with the question of nding logarithmic signatures of minimal length in nite groups. In particular, such factorizations exist for solvable, symmetric, and alternating groups. We show how
ON GENERATION OF RANDOM COVERS FOR FINITE GROUPS
"... Abstract. Covers for finite groups, a generalization of logarithmic signatures, form the basis of the ElGamallike publickey cryptosystem MST2. A relevant and open problem about the practical use of covers is the question of how to generate random covers for groups of large order. In this paper we ..."
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Abstract. Covers for finite groups, a generalization of logarithmic signatures, form the basis of the ElGamallike publickey cryptosystem MST2. A relevant and open problem about the practical use of covers is the question of how to generate random covers for groups of large order. In this paper we show the connection between this problem and the classical occupancy problem. As a consequence, we can solve the problem of generating random covers for arbitrarily large finite groups completely. We also present several experimental computer results about covers and uniform covers for some alternating groups. These results provide useful hints for generating uniform random covers.
Group Factorizations and Information Theory
, 2007
"... A factorization of a group G is a collection of subsets (A1, A2,..., Ar) such that every element g ∈ G has a unique representation g = a1 · a2 ·... · ar where ai ∈ Ai for i = 1,..., r. We shall survey several applications of group factorizations in information theory. They occur in the analysis of ..."
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A factorization of a group G is a collection of subsets (A1, A2,..., Ar) such that every element g ∈ G has a unique representation g = a1 · a2 ·... · ar where ai ∈ Ai for i = 1,..., r. We shall survey several applications of group factorizations in information theory. They occur in the analysis of syndromes of integer codes, several graphs with large girth important for LDPC codes can be constructed using group factorizations, and various cryptosystems are based on them.
The Cryptanalysis of a Public Key Implementation of Finite Group Mappings
"... Minghua Qu and S.A.Vanstone [2] have proposed a public key cryptosystem (FGM) which is based on factorisations of a binary vector space (i.e. transversal logarithmic signatures of an elementary abelian 2group). In this paper, a generalised (basisindependent) decryption algorithm is given, which sh ..."
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Minghua Qu and S.A.Vanstone [2] have proposed a public key cryptosystem (FGM) which is based on factorisations of a binary vector space (i.e. transversal logarithmic signatures of an elementary abelian 2group). In this paper, a generalised (basisindependent) decryption algorithm is given, which shows that there are many equivalent private keys, and a method of efficiently obtaining such an equivalent private key is given. The FGM cryptosystem is thus rendered insecure. Although the FGM cryptosystem is defined in terms of linear algebra, the attack given here is essentially grouptheoretic in nature. Thus this attack throws doubt on any cryptosystem which relies on the security of transversal logarithmic signatures. Key Words. Public Key Cryptosystems, Finite Group Mappings, Permutation Group Mappings, Logarithmic Signatures. This author was supported by S.E.R.C. research grant GR/H23719 1 The paper is organised as follows. Section 1 gives a description of the Finite Group Mapp...