weekly quiz

output.txt

$ time go run random-quiz-crypto.go
decryptKey 239333
decrypt 375289 -> 230801
decrypt 485994 -> 200009
decrypt 047367 -> 190020
decrypt 543573 -> 051400
decrypt 785337 -> 131504
decrypt 477107 -> 002023
decrypt 727268 -> 150000
"WHAT IS TEN MOD TWO  "

real    0m0.547s
user    0m0.499s
sys     0m0.219s

random-quiz-crypto.go

package main

import (
	"fmt"
	"math/big"
)

func bruteTwoKey(encKey, mod *big.Int) *big.Int {
	rv := big.NewInt(0)
	two := big.NewInt(1)
	two.SetInt64(2)

	// Test decrypt text
	pText := big.NewInt(12345)
	cText := big.NewInt(0)
	cText.Exp(pText, encKey, mod)
	for decK := big.NewInt(1); true; decK = decK.Add(decK, two) {
		res := big.NewInt(0)
		res = res.Exp(cText, decK, mod)
		if res.Cmp(pText) == 0 {
			rv = decK
			break
		}
	}
	return rv
}

func main() {
	// Quiz parameters
	mod := big.NewInt(799567)
	encKey := big.NewInt(5)
	cipherText := []*big.Int{
		big.NewInt(375289),
		big.NewInt(485994),
		big.NewInt(47367), // ignore leading zero, it turns this into octal
		big.NewInt(543573),
		big.NewInt(785337),
		big.NewInt(477107),
		big.NewInt(727268),
	}

	// Brute Force key
	decryptKey := bruteTwoKey(encKey, mod)
	fmt.Printf("decryptKey %s\n", decryptKey)

	// Decrypt cipherText
	plainText := []*big.Int{}
	for _, v := range cipherText {
		tmp := big.NewInt(0)
		tmp.Exp(v, decryptKey, mod)
		plainText = append(plainText, tmp)
		fmt.Printf("decrypt %06s -> %06s\n", v, tmp)
	}

	// Decode to ASCII
	humanText := []byte{}
	for _, v := range plainText {
		triplet := v.Int64()
		a := byte(triplet/10000) + 'A' - 1
		b := byte((triplet/100)%100) + 'A' - 1
		c := byte(triplet%100) + 'A' - 1
		humanText = append(humanText, a, b, c)
	}

	// Convert A-1 to space, and any unknowns to '?'
	for i, v := range humanText {

		if v == 'A'-1 {
			humanText[i] = ' '
		} else if v < 'A' || v > 'Z' {
			humanText[i] = '?'
		}
	}

	// Display
	fmt.Printf("%q\n", string(humanText[:]))
}