mathworld.wolfram.com
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MathWorld is an extensive online mathematics encyclopedia from Wolfram Research, offering clear, formula-rich articles on topics from algebra and calculus to geometry. It also covers cryptography concepts and related algorithms, making it a handy reference for math-backed cryptography learning.
More resources on Cryptography
Number Theory and Cryptography
A prominent expert in the number theory Godfrey Hardy described it in the beginning of 20th century as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the world nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this course we will start with the basics of the number theory and get to cryptographic protocols based on it. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest! As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
An Introduction to Mathematical Cryptography
An Introduction to Mathematical Cryptography - A book resource
ocw.mit.edu
MIT OpenCourseWare (OCW) offers free, openly licensed course materials from MIT across hundreds of subjects, including cryptography and computer science. Materials typically include lecture notes, assignments, exams, and often video lectures from actual MIT courses.
Cryptography I
Cryptography is an indispensable tool for protecting information in computer systems. In this course you will learn the inner workings of cryptographic systems and how to correctly use them in real-world applications. The course begins with a detailed discussion of how two parties who have a shared secret key can communicate securely when a powerful adversary eavesdrops and tampers with traffic. We will examine many deployed protocols and analyze mistakes in existing systems. The second half of the course discusses public-key techniques that let two parties generate a shared secret key. Throughout the course participants will be exposed to many exciting open problems in the field and work on fun (optional) programming projects. In a second course (Crypto II) we will cover more advanced cryptographic tasks such as zero-knowledge, privacy mechanisms, and other forms of encryption.
crypto.stanford.edu
Stanford's Crypto Group site is a hub for modern cryptography resources, featuring course materials (lecture notes, problem sets, and syllabi for Cryptography I/II) and research publications on cryptography, security, and privacy.