How much does the keyspace increase with the addition of a bit?

The increase in keyspace with the addition of a single bit is a fundamental concept in cryptography and information security. When you add an additional bit to a binary key, you double the number of possible key combinations.

For example, if you have a 3-bit key, it can represent 2^3, or 8 different combinations (000, 001, 010, 011, 100, 101, 110, 111). When you add one more bit, the key becomes a 4-bit key, which can represent 2^4, or 16 different combinations. The increase in keyspace is therefore from 8 combinations to 16 combinations, which is an increase of 100%. This doubling effect illustrates why adding a single bit dramatically increases the overall potential keyspace available for use.

Hence, when considering how much the keyspace increases with the addition of a bit, the increase is correctly represented as 100%.