// Numbas version: finer_feedback_settings
{"name": "Substitution cipher encryption/decryption", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Substitution cipher encryption/decryption", "tags": [], "metadata": {"description": "<p>A straightforward test of encrypting and decrypting an eight-letter message with the Substitution Cipher.&nbsp; Message letters are generated uniformly at random from the English alphabet and the key is a uniformly chosen random permutation of the alphabet.&nbsp; Students are expected to be able to map English letters onto elements of $\\mathbb{Z}_{26}$ in the usual order.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Suppose we wish to encrypt the (nonsense) plaintext {message} using the Substitution Cipher.</p>", "advice": "<p>a) We look up each message letter in turn in the top row of the key, and replace it by the corresponding letter in the bottom row.&nbsp; So {message[0]} is replaced by {alphabet[numberkey[numbermessage[0]]]}, which then becomes {numberkey[numbermessage[0]]}, and so on.</p>\n<p>b) This time we look up each ciphertext letter in the bottom row of the key, and replace it by the corresponding letter in the top row.&nbsp; So {ciphertext[0]} is replaced by {alphabet[map(indices(numberkey,numberciphertext[i])[0],i,0..7)[0]]}, which then becomes {map(indices(numberkey,numberciphertext[i])[0],i,0..7)[0]}, and so on.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "\"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"", "description": "", "templateType": "anything", "can_override": false}, "numbermessage": {"name": "numbermessage", "group": "Ungrouped variables", "definition": "Repeat(Random(0..25),8)", "description": "", "templateType": "anything", "can_override": false}, "message": {"name": "message", "group": "Ungrouped variables", "definition": "join(map(alphabet[x],x,numbermessage),\"\")", "description": "", "templateType": "anything", "can_override": false}, "numberkey": {"name": "numberkey", "group": "Ungrouped variables", "definition": "deal(26)", "description": "", "templateType": "anything", "can_override": false}, "key": {"name": "key", "group": "Ungrouped variables", "definition": "join(map(alphabet[x],x,numberkey),\"\")", "description": "", "templateType": "anything", "can_override": false}, "displaykey": {"name": "displaykey", "group": "Ungrouped variables", "definition": "latex(join([join([safe(\"\\\\begin{array}{cccccccccccccccccccccccccc}\"),join([join(map(alphabet[i],i,0..25),\"&\"),join(map(key[i],i,0..25),\"&\")],\"\\\\\\\\\")],\"\"),safe(\"\\\\end{array}\")],\"\"))", "description": "", "templateType": "anything", "can_override": false}, "numberciphertext": {"name": "numberciphertext", "group": "Ungrouped variables", "definition": "Repeat(Random(0..25),8)", "description": "", "templateType": "anything", "can_override": false}, "ciphertext": {"name": "ciphertext", "group": "Ungrouped variables", "definition": "join(map(alphabet[x],x,numberciphertext),\"\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet", "numbermessage", "message", "numberkey", "key", "displaykey", "numberciphertext", "ciphertext"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Encrypt the plaintext using the key $\\var{displaykey}$.&nbsp; (Express your answer as a sequence of elements of $\\mathbb{Z}_{26}$.)</p>", "correctAnswer": "matrix(map(numberkey[numbermessage[i]],i,0..7))", "correctAnswerFractions": false, "numRows": 1, "numColumns": "8", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Decrypt the ciphertext {ciphertext} using the key {displaykey}. (Express your answer as a sequence of elements of $\\mathbb{Z}_{26}$.)</p>", "correctAnswer": "matrix(map(indices(numberkey,numberciphertext[i])[0],i,0..7))", "correctAnswerFractions": false, "numRows": 1, "numColumns": "8", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Maura Paterson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7001/"}], "resources": []}]}], "contributors": [{"name": "Maura Paterson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7001/"}]}