There are well-known algorithms for binary data to string encoding exist, such as algorithms with alphabet length with radix of power 2 (base32, base64) and algorithms with alphabet length with radix not of power 2 (base85 and base91).

This library contains an implementation of algorithm for general case, that is a custom-length alphabet can be used. Here is online BaseNcoding DEMO.

Idea of developed algorithm based on base85 encoding, except of block size is not constant, but it's calculation depends on an alphabet length.

1. Calculation of block size in bits and chars.
2. Conversation of input string to byte array (using UTF8 Encoding).
3. Splitting byte array on n-bit groups.
4. Conversation of every group to radix n.
5. Tail bits processing.

For optimal block size calculation the following considerations has been used:

In this system:

• a — Length of alphabet A.
• k — Count of encoding chars.
• b — Digit radix (2 in most cases).
• n — Number of bits in radix b for representing k chars of alphabet A.
• r_values — Compression ratio (less is better).
• r_bits — Bits per char count (greater is better).
• mbc — Block max bits count.
• ⌊x⌋ — The largest integer not greater than x (floor).
• ⌈x⌉ — The smallest integer not less than x (ceiling).

See implementation in GetOptimalBitsCount method.

The most difficult problem in this project which nevertheless has been solved with only integer calculations.

int mainBitsLength = (data.Length * 8 / BlockBitsCount) * BlockBitsCount;
int tailBitsLength = data.Length * 8 - mainBitsLength;
int totalBitsLength = mainBitsLength + tailBitsLength;
int mainCharsCount = mainBitsLength * BlockCharsCount / BlockBitsCount;
int tailCharsCount = (tailBitsLength * BlockCharsCount + BlockBitsCount - 1) / BlockBitsCount;
int totalCharsCount = mainCharsCount + tailCharsCount;
int iterationCount = mainCharsCount / BlockCharsCount;

int totalBitsLength = ((data.Length - 1) * BlockBitsCount / BlockCharsCount + 8) / 8 * 8;
int mainBitsLength = totalBitsLength / BlockBitsCount * BlockBitsCount;
int tailBitsLength = totalBitsLength - mainBitsLength;
int mainCharsCount = mainBitsLength * BlockCharsCount / BlockBitsCount;
int tailCharsCount = (tailBitsLength * BlockCharsCount + BlockBitsCount - 1) / BlockBitsCount;
BigInteger tailBits = CharsToBits(data, mainCharsCount, tailCharsCount);
if (tailBits >> tailBitsLength != 0)
{
	totalBitsLength += 8;
	mainBitsLength = totalBitsLength / BlockBitsCount * BlockBitsCount;
	tailBitsLength = totalBitsLength - mainBitsLength;
	mainCharsCount = mainBitsLength * BlockCharsCount / BlockBitsCount;
	tailCharsCount = (tailBitsLength * BlockCharsCount + BlockBitsCount - 1) / BlockBitsCount;
}
int iterationCount = mainCharsCount / BlockCharsCount;

Diagram of an optimal block size and alphabet length dependence has been calculated with help of system above for mbc = 64:

Big numbers (C# BitInteger and JavaScript jsbn) used for some calculations.

Algorithm also has a parallel version.

BaseN algorithm is licensed under the Apache 2.0 License.

More detail explanation available on Russian.