Mini private key format
The mini private key format is a method of encoding a Bitcoin private key in as few as 22 characters so that it can be embedded in a small space. This private key format was first used in Casascius physical bitcoins, and is also favorable for use in QR codes. The fewer characters encoded in a QR code, the lower dot density can be used, as well as more dots allocated to error correction in the same space, significantly improving readability and resistance to damage. The mini private key format offers its own built-in check code as a small margin of protection against typos.
An example key using this encoding is S4b3N3oGqDqR5jNuxEvDwf.
Usage on a physical bitcoin
The way it might appear within a physical bitcoin is on a round card printed as follows:
Mini private keys can be imported through the following clients/services:
The current mainline ("Satoshi") client cannot currently be used to import minikeys.
The private key encoding consists of 22, 26, or 30 alphanumeric characters from the base58 alphabet used in Bitcoin. The first of the characters is always the uppercase letter S.
A simple test must be performed to determine which method shall be used:
- Add a question mark to the end of the mini private key string.
- Take the SHA256 hash of the entire string. However, we will only looking at the first two bytes of the result.
- If the first byte is 00, the string is a well-formed minikey. If the first byte is not 00, the string should be rejected as a minikey.
Example with SHA256
Here is an example with the sample private key Sz9vkwiuc5ghNWKcemKoNi66pJ6AgM.
The string "Sz9vkwiuc5ghNWKcemKoNi66pJ6AgM?" has a SHA256 value that begins with 00, so it is well-formed.
To obtain the full 256-bit private key, simply take the SHA256 hash of the entire string. There is no encoding for breaks in the string even if printed that way - the SHA256 should be taken of exactly thirty bytes.
SHA256("Sz9vkwiuc5ghNWKcemKoNi66pJ6AgM") = 68DD9613911D884866A613EE909A8C3B1877D47BF4B59350AA44ED1687FA5127
The mini private key format offers a simple typo check code. Mini private keys must be generated in a "brute force" fashion, keeping only keys that conform to the format's rules. If a key is well-formed (22, 26, or 30 Base58 characters starting with S), but fails the hash check, then it probably contains a typo.
If the SHA256 hash of the string followed by '?' doesn't result in something that begins with 0x00 or 0x01, the mini private key is not valid.
If it starts with 0x01, but the second byte is higher than the allowed maximum (0x30), the mini private key is invalid. Note that the maximum is likely to be increased as computing power advances.
Creating mini private keys
Creating mini private keys is relatively simple. One program which can create such keys is Casascius Bitcoin Utility.
Mini private keys must be created "from scratch", as the conversion from mini private key to full-size private key is one-way. In other words, there is no way to convert an existing full-size private key into a mini private key.
To create mini private keys, simply create random strings that satisfy the well-formedness requirement, and then eliminate the ones that do not pass the typo check. (This means eliminating more than 99% of the candidates.) Then use the appropriate algorithm to compute the corresponding private key, and in turn, the matching Bitcoin address. The Bitcoin address can always be computed from just the private key.
It is highly recommended to use the PBKDF2 function and select at least 4096 rounds. (This means selecting strings as keys whose SHA256(string+"?") begins with 0x0128). Mini private keys offer a minimum of entropy, so the more rounds you choose, the stronger your keys will resist advances in technology to do brute-force cracks.
The SHA256 function is provided for the convenience of hardware and software environments that offer very limited computational power, such as microcontrollers. It provides for the ability to generate a valid mini private key with, on average, 256 operations of SHA256. However, it also offers the lowest brute force attack resistance. Such keys are only suitable for situations where a "throwaway" Bitcoin address is needed, such as on a coupon or ticket where the amount will be spent soon, as opposed to an address where bitcoins will be kept long term. The strongest possible PBKDF2-based keys should always be preferred in any environment where generating them is possible.
In all cases, you must use a secure cryptographic random number generator to eliminate risks of predictability of the random strings.
The 22-character mini private key code appears to offer about 123 bits of entropy, determined as log2(58^21). (Because the first character is fixed, there are 21 symbols which can each have one of 58 values).
The 26-character version offers about 146 bits of entropy by the same calculation. The 30-character version offers over 169 bits, which exceeds the 160-bits found in a Bitcoin address.
The following code produces sample SHA256-based mini private keys in Python. For real-world use, random must be replaced with a better source of entropy, as the Python documentation for random states the function "is completely unsuitable for cryptographic purposes".
import random import hashlib BASE58 = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz' def Candidate(): """ Generate a random, well-formed mini private key. """ return('%s%s' % ('S', ''.join( [BASE58[ random.randrange(0,len(BASE58)) ] for i in range(21)]))) def GenerateKeys(numKeys = 10): """ Generate mini private keys and output the mini key as well as the full private key. numKeys is The number of keys to generate, and """ keysGenerated = 0 totalCandidates = 0 while keysGenerated < numKeys: try: cand = Candidate() # Do typo check t = '%s?' % cand # Take one round of SHA256 candHash = hashlib.sha256(t).digest() # Check if the first eight bits of the hash are 0 if candHash == '\x00': privateKey = GetPrivateKey(cand) print('\n%s\nSHA256( ): %s\nsha256(?): %s' % (cand, privateKey, candHash.encode('hex_codec'))) if CheckShortKey(cand): print('Validated.') else: print('Invalid!') keysGenerated += 1 totalCandidates += 1 except KeyboardInterrupt: break print('\n%s: %i\n%s: %i\n%s: %r\n%s: %.1f' % ('Keys Generated', keysGenerated, 'Total Candidates', totalCandidates, 'Additional Security', additionalSecurity, 'Reject Percentage', 100*(1.0-keysGenerated/float(totalCandidates)))) def GetPrivateKey(shortKey): """ Returns the hexadecimal representation of the private key corresponding to the given short key. """ if CheckShortKey(shortKey): return hashlib.sha256(shortKey).hexdigest() else: print('Typo detected in private key!') return None def CheckShortKey(shortKey): """ Checks for typos in the short key. """ if len(shortKey) != 22: return False t = '%s?' % shortKey tHash = hashlib.sha256(t).digest() # Check to see that first byte is \x00 if tHash == '\x00': return True return False