Need help with highlighted Exercise 1 & Exercise 2

Pupil Text MEP: Codes and Ciphers, Unit 12 One-Time Pads 12 One-Time Pads A one-time pad is a random collection of letters, e.g. FXIPUF, which can be used to encrypt messages with complete security (i.e.it is impossible to recover the message without knowing the key) Suppose we wish to encrypt the message SECRET. There are three main methods for doing this, all of which involve a slightly different arithmetic from normal The arithmetic is called modular arithmetic. If the result of a sum is bigger than or equal to 26, we only consider the remainder after division by 26 16 + 11 = 27 = 1 (mod 26) 11 x 5-55 -3 (mod 26) Thus and Negative numbers follow the same rule, but we add 26 repeatedly rather than subtract So -26- 2 mod 26) 26 is known as the modulus of the arithmetic. Note that 26 -0 (mod 26) You should already be familiar with this type of arithmetic when telling time for example, three hours after 11 o'clock is 11+3=14 - 2 o'clock which is the same as saying 113 14 mod 12) For this reason, modular arithmetic is also known as 'clock arithmetic We treat each letter of the alphabet as a number between 0 and 25. We can use any order we like, but a sensible one would be A 1, B -2, Y-25, Z- 0. We ignore spaces between words So using numbers our message becomes 19 5 318 5 20 We do the same to our one-time pad 6 24 9 1621 6 Pupil Text MEP: Codes and Ciphers, Unit 12 One-Time Pads 12 One-Time Pads A one-time pad is a random collection of letters, e.g. FXIPUF, which can be used to encrypt messages with complete security (i.e.it is impossible to recover the message without knowing the key) Suppose we wish to encrypt the message SECRET. There are three main methods for doing this, all of which involve a slightly different arithmetic from normal The arithmetic is called modular arithmetic. If the result of a sum is bigger than or equal to 26, we only consider the remainder after division by 26 16 + 11 = 27 = 1 (mod 26) 11 x 5-55 -3 (mod 26) Thus and Negative numbers follow the same rule, but we add 26 repeatedly rather than subtract So -26- 2 mod 26) 26 is known as the modulus of the arithmetic. Note that 26 -0 (mod 26) You should already be familiar with this type of arithmetic when telling time for example, three hours after 11 o'clock is 11+3=14 - 2 o'clock which is the same as saying 113 14 mod 12) For this reason, modular arithmetic is also known as 'clock arithmetic We treat each letter of the alphabet as a number between 0 and 25. We can use any order we like, but a sensible one would be A 1, B -2, Y-25, Z- 0. We ignore spaces between words So using numbers our message becomes 19 5 318 5 20 We do the same to our one-time pad 6 24 9 1621 6