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Comment by tlb | Hacker News Reader

It's base-62, just using the 52 alphabetics and 10 digits. Using just those characters ensures it can be typed and won't be mangled by international, HTML, or URL encodings.

>>> log(62)/log(2) * 32

190.53428193238003

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Please provide an example of base62 encoding. With base64, it is trivial to break 192 bits in a group of 6 bits each and assign one of the 64 characters to each (A-Z, a-z, 0-9, /, +). With 190 bits, how is the encoding done?

I'm sorry if I'm missing something trivial here.

Here's a hint: base10 encoding those 192 bits just means "write the number in decimal". Since 2^192 is about 6E57, that can be done in at most 58 digits.

However, it is not possible to break 192 bits into 58 groups so that each group can be coded in one of those digits. Clearly, some of the bits must end up in more than one of those digits.

base62 is similar to the base10 case, but uses 62 different digits.

If this explanation is insufficient, check http://en.wikipedia.org/wiki/Ascii85. That's for base 85, but the approach is the same.

Thanks very much. I understand the generic method now. Base64 with 192 bits is just a special case where both 192 and 64 are powers of 2, which allows simple encoding by grouping the bits.

The same way a base2 number can be represented in base10: http://www.epcc.edu/tutorialservices/valleverde/Documents/Nu...

It's no harder than converting a binary number to decimal.

But I doubt they store the 190 raw bits. Instead, the token is probably generated by appending 32 characters, each sampled randomly from the 62-character alphabet. The result has 190.53 bits of entropy.

Base62 is base64 without the '/' and '+'.

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