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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On open subgroups of p-adic algebraic groups
p-adic 代数群 开子群
2023/5/5
In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
Group-homomorphic Secret Sharing Schemes Are Group-characterizable with Normal Subgroups
homomorphic secret sharing schemes group-characterizable distribution quasi-uniform distribution
2019/5/29
A group-characterizable random variable [Chan and Yeung 2002] is induced by a joint distribution on the (left) cosets of some subgroups of a main group. A homomorphic secret sharing scheme [Benaloh 19...
Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons
RSA homomorphic encryption homomorphic threshold
2018/3/5
In contrast to related work which encrypts and acts on each bit of the input separately, our protocol compares multiple input bits simultaneously within a single ciphertext. Compared to the related pr...
Parameterization of Edwards curves on the rational field Q with given torsion subgroups
Edwards curve twisted Edwards curve torsion subgroups
2018/1/29
This paper presents the basic concepts of the Edwards curves, twisted Edwards curves and the point addition laws on these curves. The main result is the parameterization of the Edward curve with the g...
A Certain Family of Subgroups of Zn⋆ Is Weakly Pseudo-Free under the General Integer Factoring Intractability Assumption
families of computational groups weak pseudo-freeness abelian groups
2017/11/28
A Certain Family of Subgroups of Zn⋆ Is Weakly Pseudo-Free under the General Integer Factoring Intractability Assumption.
Security Analysis of ePrint Report 2016/500 "Efficient Identity-Based Encryption and Public-Key Signature from Trapdoor Subgroups"
attack trapdoor subgroup congruential equations
2016/5/30
In this short report we analyse the security of three schemes proposed by J. H. Park et al. in "Efficient Identity-Based Encryption and Public-Key Signature from Trapdoor Subgroups". The schemes make ...
Efficient Identity-Based Encryption and Public-Key Signature from Trapdoor Subgroups
identity-based encryption trapdoor subgroup RSA modulus
2016/5/24
We present a new Identity-Based Encryption (IBE) scheme from a trapdoor subgroup of Z∗n for an RSA modulus n. In a trapdoor subgroup of Z∗n, a subgroup order is hidden and can be used as a...
Groups With Two Generators Having Unsolvable Word Problem And Presentations of Mihailova Subgroups
word problem subgroup membership problem Mihailova subgroup
2016/1/8
A presentation of a group with two generators having unsolvable word problem and an
explicit countable presentation of Mihailova subgroup of F2 × F2 with finite number of generators are
given. Where...
CHARACTERISTIC CLASSES AND REPRESENTATIONS OF DISCRETE SUBGROUPS OF LIE GROUPS
CHARACTERISTIC CLASSES REPRESENTATIONS
2015/9/29
(For convenience we shall henceforth assume that n is torsionfree: by
Selberg's lemma [12] this may be accomplished by replacing TT by a subgroup of
finite index. This insures that M is a compact ...
IDEAL TRIANGLES IN EUCLIDEAN BUILDINGS AND BRANCHING TO LEVI SUBGROUPS
EUCLIDEAN BUILDINGS AND BRANCHING mathematics
2015/9/29
Let G denote a connected reductive group, de ned and split over Z, and
let M G denote a Levi subgroup. In this paper we study varieties of geodesic
triangles with xed vector-valued side-lengths ...
We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl groups
used in [H], [PR] and in [R].
HIGHER-LEVEL CANONICAL SUBGROUPS IN ABELIAN VARIETIES
ABELIAN VARIETIES CANONICAL SUBGROUPS
2015/7/6
An abeloid space over a rigid space S over a non-archimedean field k is a proper
smooth S-group A → S with connected fibers. Relative ampleness (in the sense of [C3]) gives a good notion
...
Cohomology of congruence subgroups of SL4(Z)
Matrix eisenstein series classic regular modular
2014/12/29
Let N>1 be an integer, and let Γ=Γ0(N)SL4( ) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H5(Γ; ) for a range of N and compute the action of some Hecke operat...
Cohomology of congruence subgroups of SL(4, Z) II
Congruence subgroup other boundary Betty
2014/12/24
In a previous paper [3] we computed cohomology groups H5(..0(N),C), where ..0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N. In this note we update this earlier work by exten...
COHOMOLOGY OF CONGRUENCE SUBGROUPS OF SL4(Z). III
Cohomology group group congruence sparse matrix zero matrix calculation
2014/12/24
In two previous papers we computed cohomology groups for a range of levels , where is the congruence subgroup of consisting of all matrices with bottom row congruent to mod . In this note we update th...