156_74821_ias lab studmanual 16-17

# Denoted z m suppose we wish to find modular

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, denoted Z m. Suppose we wish to find modular multiplicative inverse x of 3 modulo 11. x=3 -1 (mod 11) This is the same as finding x such that 3x= 1 (mod 11) Working in Z 11 we find one value of x that satisfies this congruence is 4 because 3.4=12= 1 (mod11) and there are no other values of x in Z 11 that satisfy this congruence. Therefore, the modular multiplicative inverse of 3 modulo 11 is 4. Experiment-8 Aim: Generate Random numbers using Linear Congruential Generator & Blum Blum Shub Generator. Description: A linear congruential sequence is a series of numbers based on the recurrence relation formula: X n = (aX n-1 + c) mod m In this formula, m is called the modulus, a is called the multiplier, and c is called the increment. It is  not difficult to imagine the resulting sequence of this formula when given different values. For  example, with a = 2, c = 3, m = 10, and a starting value of X = 5, the following sequence would be  produced: 5 3 9 1 5 3 9 1 5 3...

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Experiment-9
Aim: Convert given plaintext to ciphertext using RSA algorithm. Description: Example: 1. Select two prime numbers, p = 17 and q = 11. 2. Calculate n = pq = 17 × 11 = 187. 3. Calculate f( n ) = ( p - 1)( q - 1) = 16 × 10 = 160. 4. Select e such that e is relatively prime to f( n ) = 160 and less than f( n ); we choose e = 7. 5. Determine d such that de K 1 (mod 160) and d < 160.The correct value is d = 23, because 23 × 7 = 161 = (1 × 160) + 1; d can be calculated using the extended The example shows the use of these keys for a plaintext input of M = 88. For encryption, we need to calculate C = 88 7 mod 187. Exploiting the properties of modular arithmetic, we can do this as follows. 88 7 mod 187 = [(88 4 mod 187) × (88 2 mod 187) × (88 1 mod 187)] mod 187 88 1 mod 187 = 88 88 2 mod 187 = 7744 mod 187 = 77 88 4 mod 187 = 59,969,536 mod 187 = 132

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88 7 mod 187 = (88 × 77 × 132) mod 187 = 894,432 mod 187 = 11 For decryption, we calculate M = 1123 mod 187: 1123 mod 187 = [(11 1 mod 187) × (11 2 mod 187) × (11 4 mod 187) × (11 8 mod 187) × (11 8 mod 187)] mod 187 11 1 mod 187 = 11 11 2 mod 187 = 121 11 4 mod 187 = 14,641 mod 187 = 55 11 8 mod 187 = 214,358,881 mod 187 = 33 11 23 mod 187 = (11 × 121 × 55 × 33 × 33) mod 187 = 79,720,245 mod 187 = 88 Experiment-10
Aim: Convert given plaintext to ciphertext using Diffie-Hellman algorithm. Description: Example: PROJECTS DESCRIPTION

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1 . Design & implement a project which accomplishes Analysis of English Alphabets (Called Frequency Analysis) that occur in encryption of plain text letters to cipher text letters expressed in English language only. As per data in English language frequency analysis the letter ‘t’ occupies with 18% followed by ‘s’ and so on. This project aims to implement different classical substitution and transposition techniques and then apply frequency analysis to break the cipher text produced by any conventional encryption techniques similar to Caesar, Hill, Playfair and more. The mini project includes the experiments with concepts of Substitution, Transposition techniques and Frequency Analysis of English alphabets as containing some of the following a. Caesar Cipher b. Mono Alphabetic Cipher c. Hill Cipher d. Play Cipher e. Poly Alphabetic Cipher – Vigenere Cipher f. Poly alphabetic Cipher – Gauss Cipher g. Rail fence Technique h. Columnar Cipher

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