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[Audio] APPLICATION OF MATRIX IN ENGINEERING. APPLICATION OF MATRIX IN ENGINEERING.
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[Audio] RMD ENGINEERING COLLEGE 24MA101 - MATRICES AND CALCULUS PROJECT - 1 Done by V.Manu Shri , P.Praveena , S.Sangeetha submitted to : Dr.Rajakumari mam.
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[Audio] WHAT IS MATRICES ?. WHAT IS MATRICES ?.
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[Audio] FOR EXAMPLE : IN MATHEMATICS, A Matrices is a rectangular array or tables of numbers ,symbols or expressions with elements or entries arranged in rows and columns which is used to represent a mathematical objects.
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[Audio] APPLICATION OF MATRICES IN CRYPTOGRAPHY " A Matrix can be used as a cipher to encrypt a message " the matrix must be invertible for use un decrypting The mathematics behind symmetric encryption algorithms, such as the Advanced Encryption Standard (AES), involve operations like substitution, permutation, and modular arithmetic.
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[Audio] COMPONENTS OF CRYPTOGRAPHY ✓ ENCRYPTION ✓ DECRYPTION ✓ KEY MANAGEMENT.
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[Audio] ENCRYPTION: ❖ Definition: Encryption is the process of protecting information or data by using mathematical models to scramble it in such a way that only the parties who have the key to unscramble it can access it. ❖ Encryption is a form of data security in which information is converted to ciphertext. ❖ Formula for encryption: En(x) = (x + n) mod 26.
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[Audio] DECRYPTION: ❖ Definition: The conversion of encrypted data into its original form is called Decryption. It is generally a reverse process of encryption. It decodes the encrypted information so that an authorized user can only decrypt the data because decryption requires a secret key or password. ❖ In simple words, Decryption is the process of converting an encrypted message back to its original (readable) format. The original message is called the plaintext message. The encrypted message is called the ciphertext message. ❖ Formula for decryption: Dn(x) = (x – n) mod 26.
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[Audio] KEY MANAGEMENT: ❖ Key management refers to the processes and procedures involved in generating, storing, distributing, and managing cryptographic keys used in cryptographic algorithms to protect sensitive data. ❖ It ensures that keys used to protect sensitive data are kept safe from unauthorized access or loss. Good key management helps maintain the security of encrypted information and is important cyber threats. ❖ There are two types of key management : ➢ Distribution of public keys. ➢ Use of public-key encryption to distribute secrets..
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Sender Plaintext 10 9 Encryption key 12 2 Decryption key Receiver Plaintext Encryption Algorithm Ciphertext Decryption Algorithm Interceptor.
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[Audio] ABCDEFGHIJKLM12345678910111213NOPQRSTUVWXYZ14151617181920212223242526 ENCRYPTIONANDDECRYPTION: ❑ENCRYPTION:Converteachgroupintoastringofnumbersbyassigninganumbertoeachletterofthemessage.Remembertoassignletterstoblankspaces❑Dividethelettersofthemessageintogroupsoftwoorthree❑Converteachgroupofnumbersintocolumnmatrices. ❑Convertthecolumnmatricesintoanewsetofcolumnmatricesbymultiplyingthemwithacompatiblesquarematrixofyourchoicethathasainverse.Thisnewsetofnumbersormatricesrepresentsthecodedmessage.❑DECRYPTION:Itistheinverseoftheencryptionprocess.
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[Audio] EXAMPLE FOR ENCRYPTION AND DECRYPYION : SENDER:(Encoding) G O O D 7 15 15 4 1 0 -1 2 7 15 A = 15 4 Matrix multiplication: A = -8 30 11 8 11 8 -8 30.
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[Audio] RECEIVER:(Decoding) 8 30 11 8 Find A inverse: A^-1 = 1/|A|( adj A) A = 1 0 -1 2 2 0 A^-1 = 1/2 1 1 2 0 (Matrix multiplication) -8 30 1/2 1 1 11 8.
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[Audio] = 1/2 14 30 30 8 = 7 15 15 4 7 15 15 4 G O O D.