{"id":215,"date":"2025-07-23T00:11:45","date_gmt":"2025-07-22T17:11:45","guid":{"rendered":"https:\/\/algebra.math-ugm.id\/?p=215"},"modified":"2025-07-28T10:49:06","modified_gmt":"2025-07-28T03:49:06","slug":"7th-day-cimpa-school-2025-on-arithmetic-in-action-number-theory-and-its-applications-to-cryptography-and-coding-theory","status":"publish","type":"post","link":"https:\/\/algebra.math-ugm.id\/en\/7th-day-cimpa-school-2025-on-arithmetic-in-action-number-theory-and-its-applications-to-cryptography-and-coding-theory\/","title":{"rendered":"7th Day: CIMPA SCHOOL 2025 on Arithmetic in Action: Number Theory and its Applications to Cryptography and Coding Theory"},"content":{"rendered":"

<\/p>\n

Universitas Gadjah Mada, Yogyakarta, Indonesia<\/span><\/strong><\/p>\n

July 22, 2025<\/span><\/strong><\/p>\n

Lecturing Session<\/strong><\/span><\/h4>\n

The seventh day of CIMPA SCHOOL 2025 began with Dr. Elisa Lorenzo Garcia delivering her first lecture on Coding Theory<\/em>. She began with examples highlighting the daily need for coding theory, using parity checks and Hamming codes as motivating cases before introducing the general definitions of codes, codewords, code size, [n,k]-codes, and information rate. Dr. Garcia continued by defining the Hamming distance, discussed theoretical aspects of error correction, and presented the Singleton bound. She concluded the lecture by introducing the concept of a generator matrix of a code.<\/p>\n

\"\"<\/p>\n

The next session was led by Prof. Michel Waldschmidt, who continued his lecture on Lattices<\/em>. He began by proving the equivalence of the two definitions of lattices presented in his previous lecture and introduced the notion of quadratic forms, which led to a third definition of lattices using finitely generated subgroups.<\/span><\/p>\n

\"\"<\/p>\n

The last lecture of the day was delivered by Dr. Adeline Roux-Langlois, providing an Introduction to Lattice-Based Cryptography<\/em>. She discussed various hard problems in cryptography and introduced the Shortest Vector Problem (SVP), the approximate SVP, short integer solutions, and reduction methods. Dr. Roux-Langlois concluded her lecture by defining hash functions and explaining their applications in solving short integer solutions within cryptographic contexts.<\/p>\n

\"\"<\/p>\n

SageMath Session<\/strong><\/span><\/h4>\n

Participants engaged in hands-on SageMath activities, applying their learning by working with cryptographic algorithms such as the Caesar cipher, Vigen\u00e8re cipher, and RSA, reinforcing practical skills alongside theoretical knowledge.<\/p>\n

Extra Session<\/strong><\/span><\/h4>\n

The day concluded with participant presentations on their research, focusing on topics related to lattices and cryptography, allowing them to share progress and receive feedback from peers and instructors.<\/p>\n

\"\"<\/p>\n

<\/p>","protected":false},"excerpt":{"rendered":"

Universitas Gadjah Mada, Yogyakarta, Indonesia July 22, 2025 Lecturing Session […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-215","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/215","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/comments?post=215"}],"version-history":[{"count":2,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/215\/revisions"}],"predecessor-version":[{"id":250,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/215\/revisions\/250"}],"wp:attachment":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/media?parent=215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/categories?post=215"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/tags?post=215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}