[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-227737-en":3,"doc-seo-227737-105":30,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},227737,1099523885074,"Riley West","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",8,"Research & Report","TOPICS IN COMPUTATIONAL NUMBER THEORY AND CRYPTANALYSIS - Euclidean Lattices, Edwards Curves and Cryptographic Multilinear Maps","The thesis content lies at the intersection of number theory and cryptology, advancing mathematical cryptanalysis and arithmetic geometry through explicit, computational methods in number theory. It is organized into four main parts covering distinct research works. The first part studies cryptographic multilinear maps from graded encoding systems, focusing on the CLT13 scheme and developing high-dimensional lattice-based attacks that defeat an existing countermeasure and recover secret parameters. The second part generalizes cryptanalytic techniques around the Hidden Lattice Problem.","PhD-FSTM-2021-039  \nFaculty of Science, Technology and Medicine  \nDISSERTATION  \nDefence held on 06/07/2021 in Esch-sur-Alzette to obtain the degree of  \nDOCTEUR DE L’UNIVERSITE DU LUXEMBOURG EN MATHEMATIQUES  \nby  \nLuca Notarnicola  \nBorn on 12 October 1992 in Luxembourg (Luxembourg)  \nTOPICS IN COMPUTATIONAL NUMBER THEORY AND CRYPTANALYSIS  \nOn Euclidean Lattices, Edwards Curvesand Cryptographic Multilinear Maps  \nDissertation defence committee:  \nDr. Gabor Wiese, Dissertation supervisor Professor, Université du Luxembourg  \nDr. Jean-Sébastien Coron, Dissertation supervisor Professor, Université du Luxembourg  \nDr. Antonella Perucca, Chairman Professor, Université du Luxembourg  \nDr. Frederik Vercautern Professor, KU Leuven  \nDr. Phong Q. Nguyen  \nProfessor, Inria and DIENS PSL Paris  \n2  \nAcknowledgments  \nThankyou to my supervisors, Jean-Sébastien Coron and Gabor Wiese. I am deeply grateful for their continuous support, for guiding me with patience and passion, and for everything they taught me over the last years. Thank you, Jean-Sébastien, for introducing me to the beautiful world of cryptography; your great positivity, intuition, and exemplary simplicity in tackling problems helped me a lot. Thank you, Gabor, for shaping my interest in number theory since my Bachelor studies and supervising all my theses; your rigour and extraordinary attention to detail made me improve every day.  \nThank you to my collaborators, Jean-Sébastien Coron, Gabor Wiese, and Samuele Anni, for sharing many ideas and for all their time and efforts. It is a pleasure to work with you. Thankyou, Samuele, for the opportunity to work together, for pointing me to many interesting problems, and for the great enthusiasm during our meetings.  \nThankyou to the non-supervising jury members, Antonella Perucca, Frederik Vercauteren, and Phong Nguyen. I am sincerely thankful for your interest in my work. Thankyou, Frederik, for joining my thesis supervising committee, and the fruitful discussions.  \nThank you to my colleagues and friends, for contributing to a great working environment. I am particularly thankful to the members close to the number theory group or the Applied Crypto group, with whom I had the chance to spend my everyday life: Gabor, Antonella, Alexander, Shaunak, Samuele, Andrea, Lassina, Alexandre, Jasper, Mariagiulia, Emiliano, Daniel, Pietro, Sebastiano, Bryan, Flavio, Fabio, and Jean-Sébastien, Benoît, Moon Sung, Rajeev, Razvan, François, Vitor, Najmeh, Agnese, Lorenzo, Jim, Raluca, Paul. Thank you to myoffice mates, Jasper, Daniel, and Fabio, for the nice atmosphere. Thank you to Gerard van der Geer for his beautiful lectures during his regular visits at the department. Thank you to who preciously helped me in organizing events and trips: Guenda and Gabor, for co-organizing the Mathematical Careers Day 2018 and 2019, Robert, for your outstanding help within the DPMA-PhD representative team, and Jim and Vincent Koenig, for your valuable support in coordinating events within the SP2 (Security and Privacy for System Protection) community. Thank you to many other friends from various departments, for all the fun activities, trips, football games, dinners, and mostly, your friendship. Thank you to the secretaries Marie Leblanc, Katharina Heil and Fabienne Schmitz. I could always count on your efficiency.  \nThank you to all my family members, for always believing in me. Especially, my brother, Massimo, and my parents, Rosanna and Vito. A heartfelt thank you, for everything.  \nThis work is supported by the Luxembourg National Research Fund through the grant PRIDE15/10621687/-SPsquared.  \nLuca Notarnicola Bettembourg, May 2021  \nii  \nAbstract  \nThe content of this thesis is situated between number theory and cryptology. It contributesin several directions of mathematical cryptanalysis and arithmetic geometry, by the use of explicit and computational methods in number theory. The thesis is divided into four main parts, describing four different works.  ","cbCaipQAtWO9XN5f","https://ap.wps.com/l/cbCaipQAtWO9XN5f","pdf",1432596,1,194,"English","en",105,"# Acknowledgments\n# Abstract\n## Cryptographic multilinear maps and CLT13\n## Hidden Lattice Problem","[{\"question\":\"What is the main focus of the dissertation?\",\"answer\":\"The dissertation focuses on computational number theory and cryptanalysis, combining number-theoretic techniques with arithmetic geometry to analyze cryptographic constructions.\"},{\"question\":\"How does the thesis approach attacks on CLT13?\",\"answer\":\"It develops high-dimensional lattice reduction methods to perform new cryptanalysis against CLT13, overcoming an earlier countermeasure and recovering secret parameters.\"},{\"question\":\"What concept is highlighted in the second major work?\",\"answer\":\"The thesis isolates the Hidden Lattice Problem as a general problem that appears across cryptographic scenarios, including relations to the Hidden Subset Sum Problem.\"}]","TOPICS IN COMPUTATIONAL NUMBER THEORY AND CRYPTANALYSIS - 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