How can maths be used in code cracking and how does the methodology differ?

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USE OF MATHEMATICS IN CODE BREAKING
INTRODUCTION
Human beings have always needed for secret communications through public channels. The message has to be transformed to form that cannot be read to facilitate secret communication. The message that is unreadable is called a coded message. In technical terms, the original message is the called the plaintext while the unreadable message is called the ciphertext. The conversion of plaintext to ciphertext is called encryption while the conversion of ciphertext to plain text is called decryption. The process of encryption and decryption is called cryptography. The process of cryptography involves coming up with a method of converting the plaintext to ciphertext and recovering the plaintext from the ciphertext.
Cryptography is today used in to secure communication is phones, credit card information, PIN, and password used in web accounts. A cryptographic system is said to be secure when the plaintext cannot be deduced from the ciphertext. The process of trying to determine the plaintext from ciphertext through analysis of the cipher or the ciphertext is called cryptanalysis. In non-technical English is known as code breaking. Code breaking employs techniques from various fields of mathematics such as statistics, number theory, and differential calculus. Math is applied in identifying the extent to which a system is vulnerable, the probability of success in a certain algorithm and the actual…