#### QEEE Session On

#### Public Key Cryptography - Information Security and Cryptography

#### 16th, 20th & 22nd March, 2017

A QEEE Session on **“Public Key Cryptography - Information Security and Cryptography” **was organized through ICT under D2S (Direct to Student) on **16th, 20th & 22nd March 2017**with an objective to cover the **Fundamentals and Applications of Public Key Cryptography**. The session was hosted by **Prof. Chester Rebeiro** from **IIT Madras**. **Ms. Gargi Amoli, Assistant Professor (IT)** at** Dronacharya Group of Institutions, Greater Noida **coordinated the session as the Local Faculty Coordinator which was attended by the students of 8th semester IT and CSIT.

**Day 1: March 16, 2017**

**Prof. Chester Rebeiro** initiated the first session with a brief introduction to cryptography. He discussed the relevance of cryptography in Information Security and stated the fundamental uses of cryptography and its application in Confidentiality, Data Integrity, Authentication and Non - repudiation. He gave a short description of the process of public key encryption. With the help of an example, he demonstrated how public key encryption can be used to ensure confidentiality of data. He discussed a variant of **One Way Function** known as Trapdoor One Way Function. Using a diagram, he explained how digital signatures can be implemented to thwart non-repudiation.

**Prof. Rebeiro** continued the session with the discussion on the limitations of the public key encryption algorithms. He further discussed the mathematical aspects of cryptographic algorithms. With the help of examples, **Prof. Chester** explained the function of modulus operator. There was a discussion on **Euler - Totient Function** which counts the numbers that are relatively prime to the number of reference. He clarified the working of the function with the help of an example. The process of calculating multiplicative inverse was discussed. He then discussed the process of greatest common divisor using **Euclidian Algorithm**. Calculating gcd of two numbers using Extended Euclidean Algorithm was also discussed. At the end of the session Prof Rebeiro gave few exercises to the participants based on Euler-Totient Function and Euclidean Algorithm.

**Day 2: March 20, 2017**

**Prof. Chester Rebeiro **initiated the session with a brief recapitulation of the first day session. He summarized the basic methodologies of GCD function, Euler Totient Function and Inverse Function. He suggested that in order to understand the inner working of the **RSA algorithm**, one needs to have a clear understanding of the number theory and the basic mathematical functions. There was a discussion on the **Chinese Reminder Theorem**. He gave a brief history of RSA Algorithm. He explained the structure of the algorithm with the help of a diagram and then gave an insight to its underlying assumptions. He described the process of generating the keys using RSA algorithm for encrypting and decrypting a message. He took an example in order to clarify the process of key generation. He then pointed the relevance of Chinese Remainder Theorem in the RSA Algorithm.

**Prof. Rebeiro** continued the session with a discussion on **Square and Multiply Algorithm**. He talked about the basic steps which are involved in the algorithm. He clarified the working of the algorithm with the help of an example. He demonstrated the method of finding the prime numbers in RSA algorithm. He further answered the queries of the participants on the RSA algorithm. Most of the questions were based on the mathematical concepts of the algorithm, key generation and the attacks on RSA algorithm. Prof Rebeiro concluded the session with a discussion on the benefits and limitations of the RSA algorithm.

**Day 3: March 22, 2017**

**Prof. Chester Rebeiro **initiated the session by giving a brief recapitulation of the previous sessions. He briefed the participants with the basic steps followed in RSA algorithm. He discussed about the **Primality Test** of a number. With the help of an example, he demonstrated the procedure of finding whether a number is prime or not. He then showed the procedure of finding the prime number for RSA algorithm. He stated the probability of a number to be prime. He gave the specifications of the RSA algorithm.

**Prof. Rebeiro** gave an introduction to Randomized Algorithms. He categorized Randomized Algorithms as YES - based Randomised Algorithms and NO-based Randomized Algorithms. In YES - based algorithms the answer of YES is always correct, whereas the answer of NO may or may not be correct. In case of NO-based algorithms the answer of NO is always correct, whereas the answer of YES may or may not be correct. Then there was a discussion on finding large primes using Fermat’s Theorem. He discussed about **CarMichael Numbers** which are composite numbers that behave like prime numbers. The discussion on the CarMichael numbers was followed by a description of Strong Probable Primality Test.

**Prof Rebeiro** described the methodology of **Miller - Rabin Primality Test**, which is a YES - based primality test for composite numbers. He discussed the Pollard p-1 Factorization and wrote its pseudo code. He validated the pseudo code with the help of a test data. Then there was a discussion on the method of reducing GCD computations using Floyd’s Cycle. Prof Rebeiro explained the steps of designing an efficient factorization algorithm. He talked about the state of art of factorization techniques. He gave a brief introduction to **Digital Signatures**. He discussed the underlying factors of the technology. He explained the general scheme of Digital Signatures. He concluded the session with the discussion on the application of Digital Signatures.

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