Introduction to Algebraic Cryptography: Emphasis on Visual Cryptography

Introduction to Algebraic Cryptography: Emphasis on Visual Cryptography, A Talk by Dr Avishek Adhikari, currently a Professor at the Department of Mathematics, Presidency University, Kolkata, India. There is no doubt that cyber security is becoming an important aspect of life. The reason behind this kind of attitude is nothing but the development of technical dependency based on Internet. The Internet provides a wealth of information and services. Many activities in our daily lives now rely on the Internet, including various forms of communication, shopping, financial services, entertainment and many others. The growth in the use of the Internet, however, also presents certain risks. For the most part, the Internet is indeed private and secure, but there are a number of serious security risks. This talk will review some of those security risks and provide some practical suggestions on how to address them using mathematical tools such as Group theory, Ring theory, Field theory and linear algebra. Though these theories look very abstract, they have tremendous applications in our daily life. Digital world is one of such places where basic algebra is highly used. In our today's life we are very much fond of using digital gadgets such as mobile, tab, laptop, google glass, I-watch etc. As a result, digital security is very much essential to stop the unauthorized and unwanted intrusion of enemies into our personal connected digital world. Cryptography is one such subject which helps us in providing digital security. In the modern busy digital world, the word “cryptography” is well known to many of us. Everyday, knowingly or unknowingly, in many places we use different techniques of cryptography. Starting from the logging on a PC, sending e-mails, withdrawing money from ATM by using a PIN code, operating the locker at a bank with the help of a designated person from the bank, sending message by using a mobile phone, buying things through Internet by using a credit card, transferring money digitally from one account to another over the Internet, we are applying cryptography everywhere. If we observe carefully, we see that in every case we need to hide some information or it is necessary to transfer information secretly. So intuitively we can guess that cryptography has something to do with security. In this current talk, we shall discuss how Group theory, Ring theory, Field theory and number theory play important roles in constructing good cryptographic primitives.