Problem 1 Password length and entropy (20 marks) ASCII, short for American Standard Code for Information Interchange, is a method for encoding any character into a string of 7 bits. For example, the ASCII codes for A, 'a', and "?? are 1000001, 1100001, and 0111111, respectively?. ASCII has long been superseded by the much more modern and extensive UTF-8 encoding method; ASCII codes constitute a very small subset of UTF-8 codes. A password can only contain printable characters that appear on a standard US English keyboard. These include 26 upper case letters, 26 lower case letters, 10 numerical digits and the 32 special characters ^'".,;:!?-@#$%^&*_-+=() {} []VI. Not all ASCII codes correspond to printable characters. a. (2 marks) What is the total number of ASCII encodings of 8-character strings? b. What is the number of passwords of length 8 consisting of (i) (2 marks) any printable characters? (ii) (2 marks) lower case letters only? c. Approximately what percentage of 8-character ASCII encodings are passwords consisting of (i) (2 marks) any printable characters? (ii) (2 marks) lower case letters only? d. Assuming that each character in a password is chosen equally likely, what is the entropy of the space of passwords consisting of (i) (2 marks) 8 printable characters? (ii) (2 marks) 8 lower case letters? e. Suppose we want a password space with entropy 128, i.e. a total of 2128 passwords as- suming that all passwords are equally likely.? What is the minimum password length, i.e. the minimum number of characters in a password, to achieve this entropy, assuming that passwords consist of (i) (3 marks) any printable characters? (ii) (3 marks) lower case letters only? Problem 1 Password length and entropy (20 marks) ASCII, short for American Standard Code for Information Interchange, is a method for encoding any character into a string of 7 bits. For example, the ASCII codes for A, 'a', and "?? are 1000001, 1100001, and 0111111, respectively?. ASCII has long been superseded by the much more modern and extensive UTF-8 encoding method; ASCII codes constitute a very small subset of UTF-8 codes. A password can only contain printable characters that appear on a standard US English keyboard. These include 26 upper case letters, 26 lower case letters, 10 numerical digits and the 32 special characters ^'".,;:!?-@#$%^&*_-+=() {} []VI. Not all ASCII codes correspond to printable characters. a. (2 marks) What is the total number of ASCII encodings of 8-character strings? b. What is the number of passwords of length 8 consisting of (i) (2 marks) any printable characters? (ii) (2 marks) lower case letters only? c. Approximately what percentage of 8-character ASCII encodings are passwords consisting of (i) (2 marks) any printable characters? (ii) (2 marks) lower case letters only? d. Assuming that each character in a password is chosen equally likely, what is the entropy of the space of passwords consisting of (i) (2 marks) 8 printable characters? (ii) (2 marks) 8 lower case letters? e. Suppose we want a password space with entropy 128, i.e. a total of 2128 passwords as- suming that all passwords are equally likely.? What is the minimum password length, i.e. the minimum number of characters in a password, to achieve this entropy, assuming that passwords consist of (i) (3 marks) any printable characters? (ii) (3 marks) lower case letters only
