Ders Genel Bilgileri

Ders Kodu AKTS T+U+L Kredi Ders Türü MAT22770 7 3+0 3 Seçmeli Ders Linki (Türkçe) : Kopyala Ders Linki (İngilizce) : Kopyala Dersin Dili Türkçe Dersin Düzeyi Yüksek Lisans Öğretim Türü Örgün Öğretim Dersin Türü Seçmeli Dersin Amacı Bu dersin amacı, kriptografinin temel kavramlarını vermek, gizli ve açık anahtarlı şifreleme sistemlerini öğrencilere tanıtmak ve daha ileri düzeyde araştırma yapmak isteyen öğrenciler için gerekli alt yapıyı oluşturmaktır. Ayrıca matris teorisi konularını hatırlayıp matrisler yardımı ile şifreleme yapmaya çalışmaktır. Dersin İçeriği Matrisler ve özellikleri, Özel tipte matrisler, Kriptografi ile ilgili genel tekrar, Matrisler yardımıyla kripto, Temel kriptosistemler, temel sayılar teorisi, blok şifreleme algoritmaları: DES ve AES(Rijindeal), açık anahtarlı kriptografi:,RSA ve ayrık logaritma, Diffie Hellman anahtar değişim protokolü, dijital imzalar ve kimlik doğrulama, sır paylaşımı, Kriptografik algoritmaların etkin uygulama teknikleri, Diffie-Hellman anahtar değişimi ve ortada buluşma saldırısı. Pohlig-Hellman, Pollard’s Rho ve yan-kanal saldırıları. Dersin Ön Koşulları - Dersin Koordinatörü Matematik Bölüm Başkanlığı Dersi Verenler Prof. Dr. Özen ÖZER Dersin Yardımcıları - Staj Durumu Yok

Dersin Kaynakları

Kaynaklar [1]International Workshop on Post-Quantum Cryptography, [2]PQCrypto 2013: Post-Quantum Cryptographypp 231-242| Cite as[3]Simple Matrix Scheme for Encryption, Authors:Chengdong Tao, Adama Diene, Shaohua Tang, Jintai Ding Taşcı, D. (1999), Lineer Cebir, Selün Vakfı R. S. Varga, Matrix Iterative Analysis, Springer, 2000.F. A. Graybill, Matrices with Applications in Station,1969.Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011.Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author)Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.)Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg,Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) Notlar [1]International Workshop on Post-Quantum Cryptography, [2]PQCrypto 2013: Post-Quantum Cryptographypp 231-242| Cite as[3]Simple Matrix Scheme for Encryption, Authors:Chengdong Tao, Adama Diene, Shaohua Tang, Jintai Ding Taşcı, D. (1999), Lineer Cebir, Selün Vakfı R. S. Varga, Matrix Iterative Analysis, Springer, 2000.F. A. Graybill, Matrices with Applications in Station,1969.Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011.Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author)Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.)Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg,Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) Döküman [1]International Workshop on Post-Quantum Cryptography, [2]PQCrypto 2013: Post-Quantum Cryptographypp 231-242| Cite as[3]Simple Matrix Scheme for Encryption, Authors:Chengdong Tao, Adama Diene, Shaohua Tang, Jintai Ding Taşcı, D. (1999), Lineer Cebir, Selün Vakfı R. S. Varga, Matrix Iterative Analysis, Springer, 2000.F. A. Graybill, Matrices with Applications in Station,1969.Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011.Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author)Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.)Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg,Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) Ödev Ders notları ve kaynaklardan ilgili sorular ve araştırma ödevi

Ders Yapısı

Matematik ve Temel Bilimler % 100 Mühendislik Bilimleri % 0 Mühendislik Tasarımı % 0 Sosyal Bilimler % 0 Eğitim Bilimleri % 0 Fen Bilimleri % 0 Sağlık Bilimleri % 0 Alan Bilgisi % 0

Değerlendirme Ölçütleri Yarı Yıl Çalışmaları Sayısı Katkı Ara Sınav 1 % 30 Kısa Sınav 0 % 0 Ödev 9 % 20 Devam 0 % 0 Uygulama 0 % 0 Proje 0 % 0 Yarıyıl Sonu Sınavı 1 % 50 Arazi Çalışması 0 % 0 Atölye Çalışması 0 % 0 Laboratuvar 0 % 0 Sunum/Seminer Hazırlama 0 % 0 Toplam 11 % 100

AKTS Hesaplama İçeriği Etkinlik Sayısı Süresi (Saat) Toplam İş Yükü Ders Süresi 15 3 45 Sınıf Dışı Ç. Süresi 15 5 75 Ödevler 15 5 75 Ara Sınavlar 1 2 2 Yarıyıl Sonu Sınavı 1 3 3 Kısa Sınav 0 0 0   200 | AKTS Kredisi : 7

Ders Konuları

Hafta Konu Öğretim Yöntem ve Teknikleri Döküman 1 Kriptografinin temel sorunları Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 2 Kriptografinin temel sorunları Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 3 Matrisler Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 4 Özel Matris Tipleri Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 5 Özel Matris Tipleri Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 6 Matrislerle Homojen Lineer Denklem Sistemlerinin Çözümleri Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 7 Matrislerle Homojen Olmayan Lineer Denklem Sistemlerinin Çözümleri Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 8 Ara Sınav Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 9 Afin Şifreler Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 10 Hill Şifreler Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 11 Asalların Kriptografideki Önemi Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 12 Kriptoda matris uygulamaları Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 13 Kriptoda matris kullanımı Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 14 Matrisler tarafından oluşturulan kriptografiye örnekler Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 15 Genel özet ve problem çözme Anlatım ve Soru-Cevap F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.) 16 Final Sınavı AnlatımTartışmaSoru-YanıtSorun/Problem Çözme F. A. Graybill, Matrices with Applications in Station,1969. Fundamentals of Matrix Algebra, Gregory Hartman, Virginia Military Institute, 2011. Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics) 2007th Edition by James E. Gentle Making, Breaking Codes: Introduction to Cryptology 1st Edition , by Paul Garrett (Author) Lectures on Data Security: Modern Cryptology in Theory and Practice Volume: Author(s): Mihir Bellare (auth.), Ivan Bjerre Damgård (eds.) Fundamentals of cryptology Volume: Author(s): Henk C.A. van Tilborg, Cryptology and Computational Number Theory Volume: Author(s): Carl Pomerance (ed.)

Dersin Öğrenme Çıktıları: Bu dersin başarılı bir şekilde tamamlanmasıyla öğrenciler şunları yapabileceklerdir:

# Açıklama 1 Öğrenciler, Kriptografinin ne olduğunu ve nasıl kullanılabileceğini öğreneceklerdir. 2 Öğrenciler matris yapılarını öğrenecekler 3 Öğrenciler doğrusal denklem sistemlerinin çözümlerini nasıl bulacağımızı öğreneceklerdir. 4 Öğrenciler, matrislerin kriptografideki uygulamalarını öğreneceklerdir. 5 Öğrenciler kriptoda matrislerin kullanımını öğrenecekler

Dersin Program Çıktılarına Katkısı

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 Ö1 5 5 4 5 5 5 5 4 5 5 5 5 Ö2 5 5 4 5 5 5 5 4 5 5 5 5 Ö3 5 5 4 5 5 5 5 4 5 5 5 5 Ö4 5 5 4 5 5 5 5 4 5 5 5 5 Ö5 5 5 4 5 5 5 5 4 5 5 5 5

Katkı Düzeyi: 0:Yok     1:Çok Düşük     2:Düşük     3:Orta     4:Yüksek     5:Çok Yüksek