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O L Mangasarian - One of the best experts on this subject based on the ideXlab platform.

  • probability of unique Integer Solution to a system of linear equations
    European Journal of Operational Research, 2011
    Co-Authors: O L Mangasarian, Benjamin Recht
    Abstract:

    We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient conditions for the existence of a unique Solution to the system that is Integer: x [set membership, variant] {-1, 1}n. We achieve this by reformulating the problem as a linear program and deriving necessary and sufficient conditions for the Integer Solution to be the unique primal optimal Solution. We show that as long as m is larger than n/2, then the linear programming reformulation succeeds for most instances, but if m is less than n/2, the reformulation fails on most instances. We also demonstrate that these predictions match the empirical performance of the linear programming formulation to very high accuracy.

  • probability of unique Integer Solution to a system of linear equations
    European Journal of Operational Research, 2011
    Co-Authors: O L Mangasarian, Benjamin Recht
    Abstract:

    Abstract We consider a system of m linear equations in n variables Ax  =  d and give necessary and sufficient conditions for the existence of a unique Solution to the system that is Integer: x  ∈ {−1, 1} n . We achieve this by reformulating the problem as a linear program and deriving necessary and sufficient conditions for the Integer Solution to be the unique primal optimal Solution. We show that as long as m is larger than n /2, then the linear programming reformulation succeeds for most instances, but if m is less than n /2, the reformulation fails on most instances. We also demonstrate that these predictions match the empirical performance of the linear programming formulation to very high accuracy.

  • uniqueness of Integer Solution of linear equations
    Optimization Letters, 2010
    Co-Authors: O L Mangasarian, Michael C Ferris
    Abstract:

    We consider the system of m linear equations in n Integer variables Ax = d and give sufficient conditions for the uniqueness of its Integer Solution x ∈ {−1, 1}n by reformulating the problem as a linear program. Necessary and sufficient uniqueness characterizations of ordinary linear programming Solutions are utilized to obtain sufficient uniqueness conditions such as the intersection of the kernel of A and the dual cone of a diagonal matrix of ±1’s is the origin in Rn. This generalizes the well known condition that ker(A) = 0 for the uniqueness of a non-Integer Solution x of Ax = d. A zero maximum of a single linear program ensures the uniqueness of a given Integer Solution of a linear equation.

Benjamin Recht - One of the best experts on this subject based on the ideXlab platform.

  • probability of unique Integer Solution to a system of linear equations
    European Journal of Operational Research, 2011
    Co-Authors: O L Mangasarian, Benjamin Recht
    Abstract:

    Abstract We consider a system of m linear equations in n variables Ax  =  d and give necessary and sufficient conditions for the existence of a unique Solution to the system that is Integer: x  ∈ {−1, 1} n . We achieve this by reformulating the problem as a linear program and deriving necessary and sufficient conditions for the Integer Solution to be the unique primal optimal Solution. We show that as long as m is larger than n /2, then the linear programming reformulation succeeds for most instances, but if m is less than n /2, the reformulation fails on most instances. We also demonstrate that these predictions match the empirical performance of the linear programming formulation to very high accuracy.

  • probability of unique Integer Solution to a system of linear equations
    European Journal of Operational Research, 2011
    Co-Authors: O L Mangasarian, Benjamin Recht
    Abstract:

    We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient conditions for the existence of a unique Solution to the system that is Integer: x [set membership, variant] {-1, 1}n. We achieve this by reformulating the problem as a linear program and deriving necessary and sufficient conditions for the Integer Solution to be the unique primal optimal Solution. We show that as long as m is larger than n/2, then the linear programming reformulation succeeds for most instances, but if m is less than n/2, the reformulation fails on most instances. We also demonstrate that these predictions match the empirical performance of the linear programming formulation to very high accuracy.

Dung Hoang Duong - One of the best experts on this subject based on the ideXlab platform.

  • Identity-Based Linkable Ring Signatures From Lattices
    IEEE Access, 2021
    Co-Authors: Dung Hoang Duong, Willy Susilo, Kazuhide Fukushima, Shinsaku Kiyomoto
    Abstract:

    Linkable ring signatures is a useful cryptographic tool for constructing applications such as ones relative to electronic voting (e-voting), digital cashes (e-cashes) as well as cloud computing. Equipped with linkable ring signatures, e-voting, e-cash systems can simultaneously enjoy the privacy and the unreusability properties thanks to the anonymity and the linkability of linkable ring signatures. Likewise, cloud servers can enjoy a privacy-preserving ability, a flexible access control and an efficient security management with linkable ring signatures. Moreover, linkable ring signatures built in the identity-based setting would help to remove the expense of using the conventional public key infrastructure and also could be applied to the user management. This primitive hence would be suitable for huge-scale applications. In this paper, we present the first identity-based linkable ring signatures (IdLRS) in both Integer lattice and ideal lattice setting. The proposed IdLRS is proved secure in the random oracle model and based on the hardness of the short Integer Solution and ring short Integer Solution assumption. We also implement the proposed idLRS as a proof of concept and then do some experiments to evaluate the running times and the sizes.

  • a blind ring signature based on the short Integer Solution problem
    Workshop on Information Security Applications, 2019
    Co-Authors: Dung Hoang Duong, Willy Susilo
    Abstract:

    A blind ring signature scheme is a combination of a ring signature and a blind signature, which allows not only any member of a group of signers to sign on a message on behalf of the group without revealing its identity but also the user who possesses the message to blind it before sending to the group to be signed. Blind ring signature schemes are essential components in e-commercial, e-voting etc. In this paper, we propose the first blind ring signature scheme based on lattices. More precisely, our proposed scheme is proven to be secure in random oracle model under the hardness of the short Integer Solution (SIS) problem.

  • A Blind Signature from Module Latices
    2019 IEEE Conference on Dependable and Secure Computing (DSC), 2019
    Co-Authors: Huy Quoc Le, Willy Susilo, Thanh Xuan Khuc, Minh Kim Bui, Dung Hoang Duong
    Abstract:

    Since its birth by Chaum, blind signatures have become one of the fundamental components in the so-called e-cash or e-voting. The scheme ensures a message to be blinded before being signed. Among all lattice-based signatures submitted to NIST post-quantum cryptographic standardization, Dilithium is a very promising candidate. The scheme has some advantages such as simple to implement securely, conservative with parameters and minimal in total size of public key and signature. In this paper, we propose a blind signature scheme based on the framework of Dilithium in order to take advantages of Dilithium. The proposed scheme is blind and one-more unforgeable secure in the random oracle model under the hardness of the module Learning with Errors problem MLWE and the module short Integer Solution problem MSIS.

Willy Susilo - One of the best experts on this subject based on the ideXlab platform.

  • Identity-Based Linkable Ring Signatures From Lattices
    IEEE Access, 2021
    Co-Authors: Dung Hoang Duong, Willy Susilo, Kazuhide Fukushima, Shinsaku Kiyomoto
    Abstract:

    Linkable ring signatures is a useful cryptographic tool for constructing applications such as ones relative to electronic voting (e-voting), digital cashes (e-cashes) as well as cloud computing. Equipped with linkable ring signatures, e-voting, e-cash systems can simultaneously enjoy the privacy and the unreusability properties thanks to the anonymity and the linkability of linkable ring signatures. Likewise, cloud servers can enjoy a privacy-preserving ability, a flexible access control and an efficient security management with linkable ring signatures. Moreover, linkable ring signatures built in the identity-based setting would help to remove the expense of using the conventional public key infrastructure and also could be applied to the user management. This primitive hence would be suitable for huge-scale applications. In this paper, we present the first identity-based linkable ring signatures (IdLRS) in both Integer lattice and ideal lattice setting. The proposed IdLRS is proved secure in the random oracle model and based on the hardness of the short Integer Solution and ring short Integer Solution assumption. We also implement the proposed idLRS as a proof of concept and then do some experiments to evaluate the running times and the sizes.

  • a blind ring signature based on the short Integer Solution problem
    Workshop on Information Security Applications, 2019
    Co-Authors: Dung Hoang Duong, Willy Susilo
    Abstract:

    A blind ring signature scheme is a combination of a ring signature and a blind signature, which allows not only any member of a group of signers to sign on a message on behalf of the group without revealing its identity but also the user who possesses the message to blind it before sending to the group to be signed. Blind ring signature schemes are essential components in e-commercial, e-voting etc. In this paper, we propose the first blind ring signature scheme based on lattices. More precisely, our proposed scheme is proven to be secure in random oracle model under the hardness of the short Integer Solution (SIS) problem.

  • A Blind Signature from Module Latices
    2019 IEEE Conference on Dependable and Secure Computing (DSC), 2019
    Co-Authors: Huy Quoc Le, Willy Susilo, Thanh Xuan Khuc, Minh Kim Bui, Dung Hoang Duong
    Abstract:

    Since its birth by Chaum, blind signatures have become one of the fundamental components in the so-called e-cash or e-voting. The scheme ensures a message to be blinded before being signed. Among all lattice-based signatures submitted to NIST post-quantum cryptographic standardization, Dilithium is a very promising candidate. The scheme has some advantages such as simple to implement securely, conservative with parameters and minimal in total size of public key and signature. In this paper, we propose a blind signature scheme based on the framework of Dilithium in order to take advantages of Dilithium. The proposed scheme is blind and one-more unforgeable secure in the random oracle model under the hardness of the module Learning with Errors problem MLWE and the module short Integer Solution problem MSIS.

Felipe Caro - One of the best experts on this subject based on the ideXlab platform.

  • optimizing long term production plans in underground and open pit copper mines
    Operations Research, 2012
    Co-Authors: Rafael Epstein, Marcel Goic, Andres Weintraub, Jaime Catalan, Pablo Santibaoez, Rodolfo Urrutia, Raul Cancino, Sergio Gaete, Augusto Aguayo, Felipe Caro
    Abstract:

    We present a methodology for long-term mine planning based on a general capacitated multicommodity network flow formulation. It considers underground and open-pit ore deposits sharing multiple downstream processing plants over a long horizon. The purpose of the model is to optimize several mines in an integrated fashion, but real size instances are hard to solve due to the combinatorial nature of the problem. We tackle this by solving the relaxation of a tight linear formulation, and we round the resulting near-Integer Solution with a customized procedure. The model has been implemented at Codelco, the largest copper producer in the world. Since 2001, the system has been used on a regular basis and has increased the net present value of the production plan for a single mine by 5%. Moreover, integrating multiple mines provided an additional increase of 3%. The system has allowed planners to evaluate more scenarios. In particular, the model was used to study the option of delaying by four years the conversion of Chiquicamata, Codelco's largest open-pit mine, to underground operations.