Statistical Approach to Simple

Polyalphabetic Substitution Cipher

Speaker: Lokesh R

Venue : HSB 210 (S.N. Bose Hall)

Date : 12th April, 2019

Time : 5.15 p.m.

Abstract

Monoalphabetic substitution ciphers are simple way to encrypt a message where each alphabet is substituted by ciphertext alphabet. Given below is a simple substitution mapping where each letter is replaced by its neighbour.

These kind of ciphers, though used for a long time, are considered very weak by today’s standards. Every language has a specific frequency signature for the occurrence of each letter or combination of letters. In English language, letters E, T, A and O are the most common while Z, Q and X are rare. Using such information, one might be able to guess the mapping between the ciphertext alphabets and the plaintext alphabets. This kind of analysis is known as frequency analysis and it exploits the statistics of the plaintext language. The typical distribution of letters in English languages can be seen in the figure.

(Queen Mary of Scots conspiracy to assassinate Queen Elizabeth I was deciphered by frequency analysis which eventually led to her execution in 1587) In polyalphabetic substitution ciphers same letter say, “A” could be encrypted using different ciphertext alphabet depending on the location of its occurrence in the text using a key. If the key is “SUGAR”, then “A” gets mapped to “S” for the first position, “A” gets mapped to “U” in second position and so on. Since, same alphabet gets mapped to multiple alphabets in ciphertext alphabet, the frequency signature gets smeared off. Hence, frequency analysis would not be useful directly. In this talk, we will consider a simple cipher of this kind and take a statistical approach to handle such a cipher.

About the speaker

Lokesh R is a project associate at the Department of Chemical Engineering at IIT Madras. He is working on Errors in Variables Framework under Dr. Arun Tangirala and Dr. Shankar Narasimhan in a project supported by Robert Bosch Engineering India. Prior to this, he graduated with a Dual Degree (Naval Architecture and Ocean Engineering) from IIT Madras, 2005, Masters (Applied Mathematics and Statistics) from SUNY, Stony Brook University, 2009 and worked at Research and Development at Bloomberg LP.