Vigenère cipher

Computer Science Level 1

Which of the following keys would yield approximately 300 million encoding combinations for a given message using a Vigenère cipher ?

CAKE COFFEE EGG FOOTBALL MOVIE

2 solutions

Karleigh Moore
May 22, 2016

FOOTBALL has $8$ letters which yields $26^8 = 208,827,064,576$ possible combinations, which is roughly 209 billion.

CAKE has $4$ letters which yields $26^4 = 456,976$ possible combinations, which is roughly 457 thousand.

COFFEE has $6$ letters which yields $26^6 = 308,915,776$ possible combinations, which is roughly 309 million.

EGG has $3$ letters which yields $26^3 = 17,576$ possible combinations, which is roughly 18 thousand.

MOVIE has $5$ letters which yields $26^5 = 11,881,376$ possible combinations, which is roughly 12 million.

309 million is closest to 300 million, so COFFEE is the correct answer.

But coffee has repeated letters so it actually only has 4 distinct letters

Siva Budaraju - 3 years, 11 months ago

I agree with you. Football also has repeating letters also EGG.

B D - 1 year, 2 months ago

Noel Lo
May 11, 2017

Alternatively $\frac{log (3*10^8)}{log (26)}=5.99=6$ Therefore, the word should have six letters.

$=>\boxed{COFFEE}$