Chameleon Hash Functions and One-Time Signature Schemes from Inner Automorphism Groups

Simply reducible groups are closely related to the eigenvalue problems in quantum theory and molecular symmetry in chemistry. Classification of simply reducible groups is still an open problem which is interesting to physicists. Since there are not many examples of simply reducible groups in literature at the moment, we try to find some examples of simply reducible groups as candidates for the classification. By studying the automorphism and inner automorphism groups of symmetric groups, dihedral groups, Clifford groups and Coxeter groups, we find some new examples of candidates. We use the computer algebra system GAP to get most of these automorphism and inner automorphism groups.

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The finite inner automorphism groups of division rings

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410007359x ◽

1995 ◽

Vol 118 (2) ◽

pp. 207-213 ◽

Cited By ~ 2

Author(s):

M. Shirvani

Keyword(s):

Finite Groups ◽

Galois Theory ◽

Automorphism Groups ◽

Outer Automorphism ◽

Commutative Field ◽

Division Rings ◽

Inner Automorphism ◽

Projective Representations ◽

Inner Automorphisms ◽

A Finite Group

Let G be a finite group of automorphisms of an associative ring R. Then the inner automorphisms (x↦ u−1xu = xu, for some unit u of R) contained in G form a normal subgroup G0 of G. In general, the Galois theory associated with the outer automorphism group G/G0 is quit well behaved (e.g. [7], 2·3–2·7, 2·10), while little group-theoretic restriction on the structure of G/G0 may be expected (even when R is a commutative field). The structure of the inner automorphism groups G0 does not seem to have received much attention so far. Here we classify the finite groups of inner automorphisms of division rings, i.e. the finite subgroups of PGL (1, D), where D is a division ring. Such groups also arise in the study of finite collineation groups of projective spaces (via the fundamental theorem of projective geometry, cf. [1], 2·26), and provide examples of finite groups having faithful irreducible projective representations over fields.

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Tightly-Secure Signatures from Chameleon Hash Functions

Lecture Notes in Computer Science - Public-Key Cryptography -- PKC 2015 ◽

10.1007/978-3-662-46447-2_12 ◽

2015 ◽

pp. 256-279 ◽

Cited By ~ 26

Author(s):

Olivier Blazy ◽

Saqib A. Kakvi ◽

Eike Kiltz ◽

Jiaxin Pan

Keyword(s):

Hash Functions ◽

Chameleon Hash

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Tweaking TBE/IBE to PKE Transforms with Chameleon Hash Functions

Applied Cryptography and Network Security - Lecture Notes in Computer Science ◽

10.1007/978-3-540-72738-5_21 ◽

2007 ◽

pp. 323-339 ◽

Cited By ~ 21

Author(s):

Rui Zhang

Keyword(s):

Hash Functions ◽

Chameleon Hash

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APPROXIMATELY INNER FLOWS ON SEPARABLE C*-ALGEBRAS

Reviews in Mathematical Physics ◽

10.1142/s0129055x02001284 ◽

2002 ◽

Vol 14 (07n08) ◽

pp. 649-673 ◽

Cited By ~ 6

Author(s):

AKITAKA KISHIMOTO

Keyword(s):

Irreducible Representation ◽

Von Neumann Algebra ◽

Automorphism Groups ◽

Unitary Groups ◽

Type I ◽

Von Neumann ◽

C Algebra ◽

C Algebras ◽

Inner Automorphism ◽

Uniformly Continuous

We present two types of result for approximately inner one-parameter automorphism groups (referred to as AI flows hereafter) of separable C*-algebras. First, if there is an irreducible representation π of a separable C*-algebra A such that π(A) does not contain non-zero compact operators, then there is an AI flow α such that π is α-covariant and α is far from uniformly continuous in the sense that α induces a flow on π(A) which has full Connes spectrum. Second, if α is an AI flow on a separable C*-algebra A and π is an α-covariant irreducible representation, then we can choose a sequence (hn) of self-adjoint elements in A such that αt is the limit of inner flows Ad eithn and the sequence π(eithn) of one-parameter unitary groups (referred to as unitary flows hereafter) converges to a unitary flow which implements α in π. This latter result will be extended to cover the case of weakly inner type I representations. In passing we shall also show that if two representations of a separable simple C*-algebra on a separable Hilbert space generate the same von Neumann algebra of type I, then there is an approximately inner automorphism which sends one into the other up to equivalence.

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A Characterization of Chameleon Hash Functions and New, Efficient Designs

Journal of Cryptology ◽

10.1007/s00145-013-9155-8 ◽

2013 ◽

Vol 27 (4) ◽

pp. 799-823 ◽

Cited By ~ 10

Author(s):

Mihir Bellare ◽

Todor Ristov

Keyword(s):

Hash Functions ◽

Chameleon Hash

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ON AUTOMORPHISMS OF THE ENDOMORPHISM SEMIGROUP OF A FREE UNIVERSAL ALGEBRA

International Journal of Algebra and Computation ◽

10.1142/s0218196707003974 ◽

2007 ◽

Vol 17 (05n06) ◽

pp. 1085-1106 ◽

Cited By ~ 5

Author(s):

G. MASHEVITZKY ◽

B. I. PLOTKIN

Keyword(s):

Lie Algebras ◽

Universal Algebra ◽

Automorphism Groups ◽

Endomorphism Semigroup ◽

Universal Algebras ◽

Free Lie Algebras ◽

Inner Automorphism ◽

Groups Of Automorphisms ◽

Inner Automorphisms

Let U be a universal algebra. An automorphism α of the endomorphism semigroup of U defined by α(φ) = sφs-1 for a bijection s : U → U is called a quasi-inner automorphism. We characterize bijections on U defining such automorphisms. For this purpose, we introduce the notion of a pre-automorphism of U. In the case when U is a free universal algebra, the pre-automorphisms are precisely the well-known weak automorphisms of U. We also provide different characterizations of quasi-inner automorphisms of endomorphism semigroups of free universal algebras and reveal their structure. We apply obtained results for describing the structure of groups of automorphisms of categories of free universal algebras, isomorphisms between semigroups of endomorphisms of free universal algebras, automorphism groups of endomorphism semigroups of free Lie algebras etc.

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