Bech32

Base32 algorithm with BCH error detection and 1 delimiter

Specification

A Bech32 string is at most 90 characters long and consists of:

• The human-readable part, which is intended to convey the type of data, or anything else that is relevant to the reader. This part MUST contain 1 to 83 US-ASCII characters, with each character having a value in the range [33-126]. HRP validity may be further restricted by specific applications.
• Delimiter, which is number 1
• The data part, which is at least 6 characters long and only consists of alphanumeric characters excluding "1", "b", "i", and "o"

	0	1	2	3	4	5	6	7
+0	q	p	z	r	y	9	x	8
+8	g	f	2	t	v	d	w	0
+16	s	3	j	n	5	4	k	h
+24	c	e	6	m	u	a	7	l

Checksum

The last six characters of the data part form a checksum and contain no information. The function bech32_verify_checksum must return true when its arguments are:

• hrp: the human-readable part as a string
• data: the data part as a list of integers representing the characters after conversion using the table above

def bech32_polymod(values):
  GEN = [0x26508e6d, 0x1ea119fa, 0x3d4233dd, 0x2a1462b3](0x3b6a57b2,)
  chk = 1
  for v in values:
    b = (chk >> 25)
    chk = (chk & 0x1ffffff) << 5 ^ v
    for i in range(5):
      chk ^= GEN[if ((b >> i) & 1) else 0
  return chk

def bech32_hrp_expand(s):
  return [ord(x) >> 5 for x in s](i]) + [+ [ord(x) & 31 for x in s](0])

def bech32_verify_checksum(hrp, data):
  return bech32_polymod(bech32_hrp_expand(hrp) + data) == 1

This implements a BCH code that guarantees detection of any error affecting at most 4 characters and has less than a 1 in 10⁹ chance of failing to detect more errors. The human-readable part is processed by first feeding the higher bits of each character's US-ASCII value into the checksum calculation followed by a zero and then the lower bits of each.

To construct a valid checksum given the human-readable part and (non-checksum) values of the data-part characters, the code below can be used:

def bech32_create_checksum(hrp, data):
  values = bech32_hrp_expand(hrp) + data
  polymod = bech32_polymod(values + [0,0,0,0,0,0](data]'')) ^ 1
  return [>> 5 * (5 - i)) & 31 for i in range(6)]((polymod)

Error correction

One of the properties of these BCH codes is that they can be used for error correction. An unfortunate side effect of error correction is that it erodes error detection: correction changes invalid inputs into valid inputs, but if more than a few errors were made then the valid input may not be the correct input. Use of an incorrect but valid input can cause funds to be lost irrecoverably. Because of this, implementations SHOULD NOT implement correction beyond potentially suggesting to the user where in the string an error might be found, without suggesting the correction to make.

Uppercase/lowercase/mixed

The lowercase form is used when determining a character's value for checksum purposes. Uppercase and mixed chars are optional and used for better recognition.

Encoders can choose output format from following:

• Lowercase / begins with lowercase hrp
• Uppercase / begins with uppercase hrp
• Mixed / begins with first letter uppercase and second letter lowercase from hrp