{"id":23166,"date":"2024-06-26T14:21:26","date_gmt":"2024-06-26T12:21:26","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/?post_type=research-groups&#038;p=23166"},"modified":"2024-06-26T14:25:03","modified_gmt":"2024-06-26T12:25:03","slug":"research","status":"publish","type":"research-groups","link":"https:\/\/www.uni.lu\/fstm-en\/research-groups\/computational-number-theory__trashed\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<div class=\"section py-0 static\">\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><!-- SecondaryNavigationMirror --><div class=\"js-secondary-nav--sticky wp-block-unilux-blocks-secondary-navigation\" id=\"9eccd416-fd9a-4da6-be74-26bcb269ac47\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button class=\"secondary-nav__button btn btn-solid--primary w-full\" aria-expanded=\"false\" aria-controls=\"secondary-navigation__list\" title=\"The selected page is Overview\" type=\"button\">\n            <span class=\"btn__name mr-auto\">Overview<\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n            <\/svg>\n        <\/button>\n\n        <ul id=\"secondary-navigation__list\" class=\"secondary-nav__list\">\n            <li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/computational-number-theory\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Overview<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/computational-number-theory\/research\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Research<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/computational-number-theory\/people\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">People<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/computational-number-theory\/join-us\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Join us<\/span>\n    <\/a>\n<\/li>\n        <\/ul>\n    <\/nav>\n<\/div>\n<!-- end SecondaryNavigationMirror --><\/div><\/section>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<p>The Computational Number Theory group is especially interested in three different research questions:<\/p>\n\n\n\n<ol class=\"ulux-list\">\n<li class=\"ulux-list-item\">Analysing the complexity of the Simultaneous Chinese Remainder problem involves examining how difficult it is to solve when compared to the classical Chinese Remainder Theorem (CRT). In this generalized version, instead of having a unique residue as in CRT, we deal with a set of possible residues. The challenge lies in determining practical algorithms to solve this problem efficiently, considering several factors such as conditions for moduli, residue sets, and the desired outcome.<\/li>\n\n\n\n<li class=\"ulux-list-item\">There are indications that solutions to the Simultaneous Chinese Remainder problem could offer new avenues for addressing the integer factorization problem.<\/li>\n\n\n\n<li class=\"ulux-list-item\">Lattice basis reduction is a fundamental problem in computational number theory. Our research group investigates the extent to which graph-based approaches can contribute to efficiently solving this problem in number theory.<\/li>\n<\/ol>\n<\/div><\/section>\n<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":51,"featured_media":0,"parent":3591,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Computational Number Theory","uluxPrePostTitle":"Research Group","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false},"field-of-interest":[],"organisation":[],"authorship":[51,133,132,130,223],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - 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