词条 | Luhn algorithm | |||||||||||||||||||||||||||||||||||||
释义 |
The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after IBM scientist Hans Peter Luhn, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the United States, Canadian Social Insurance Numbers, Israel ID Numbers, Greek Social Security Numbers (ΑΜΚΑ), and survey codes appearing on [https://commons.wikimedia.org/wiki/File:McDonalds_Receipt_Luhn_Algorithm.png McDonald's], [https://commons.wikimedia.org/wiki/File:Taco_Bell_Receipt_Luhn_Algorithm.png Taco Bell], and [https://commons.wikimedia.org/wiki/File:Tractor_Supply_Receipt_Luhn_Algorithm.png Tractor Supply Co.] receipts. It was created by IBM scientist Hans Peter Luhn and described in U.S. Patent No. 2,950,048, filed on January 6, 1954, and granted on August 23, 1960. The algorithm is in the public domain and is in wide use today. It is specified in ISO/IEC 7812-1.[1] It is not intended to be a cryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers. DescriptionThe formula verifies a number against its included check digit, which is usually appended to a partial account number to generate the full account number. This number must pass the following test:
Assume an example of an account number "7992739871" that will have a check digit added, making it of the form 7992739871x:
The sum of all the digits in the third row is 67+x. The check digit (x) is obtained by computing the sum of the non-check digits then computing 9 times that value modulo 10 (in equation form, ((67 × 9) mod 10)). In algorithm form:
(Alternative method) The check digit (x) is obtained by computing the sum of the other digits (third row) then subtracting the units digit from 10 (67 => Units digit 7; 10 − 7 = check digit 3). In algorithm form:
This makes the full account number read 79927398713. Each of the numbers 79927398710, 79927398711, 79927398712, 79927398713, 79927398714, 79927398715, 79927398716, 79927398717, 79927398718, 79927398719 can be validated as follows.
Alternately, you can use the same checksum creation algorithm, ignoring the checksum already in place as if it had not yet been calculated. Then calculate the checksum and compare this calculated checksum to the original checksum included with the credit card number. If the included checksum matches the calculated checksum, then the number is valid. Strengths and weaknessesThe Luhn algorithm will detect any single-digit error, as well as almost all transpositions of adjacent digits. It will not, however, detect transposition of the two-digit sequence 09 to 90 (or vice versa). It will detect 7 of the 10 possible twin errors (it will not detect 22 ↔ 55, 33 ↔ 66 or 44 ↔ 77). Other, more complex check-digit algorithms (such as the Verhoeff algorithm and the Damm algorithm) can detect more transcription errors. The Luhn mod N algorithm is an extension that supports non-numerical strings. Because the algorithm operates on the digits in a right-to-left manner and zero digits affect the result only if they cause shift in position, zero-padding the beginning of a string of numbers does not affect the calculation. Therefore, systems that pad to a specific number of digits (by converting 1234 to 0001234 for instance) can perform Luhn validation before or after the padding and achieve the same result. Prepending a 0 to odd-length numbers makes it possible to process the number from left to right rather than right to left, doubling the odd-place digits. The algorithm appeared in a US Patent[2] for a hand-held, mechanical device for computing the checksum. It was therefore required to be rather simple. The device took the mod 10 sum by mechanical means. The substitution digits, that is, the results of the double and reduce procedure, were not produced mechanically. Rather, the digits were marked in their permuted order on the body of the machine. Implementation examplesPseudocodefunction checkLuhn(string purportedCC) { int sum := integer(purportedCC[length(purportedCC)-1]) int nDigits := length(purportedCC) int parity := nDigits modulus 2 for i from 0 to nDigits - 2 { int digit := integer(purportedCC[i]) if i modulus 2 = parity digit := digit × 2 if digit > 9 digit := digit - 9 sum := sum + digit } return (sum modulus 10) = 0 } C#include bool checkLuhn(const char *pNumber) { int nSum = 0; int nDigits = strlen(pNumber); int nParity = (nDigits-1) % 2; char cDigit[2] = "\\0"; for (int i = nDigits; i > 0 ; i--) { cDigit[0] = pNumber[i-1]; int nDigit = atoi(cDigit); if (nParity == i % 2) nDigit = nDigit * 2; nSum += nDigit/10; nSum += nDigit%10; } return 0 == nSum % 10; } C#public static bool check(string ccNumber) { int sum = 0; int n; bool alternate = false; char[] nx = ccNumber.ToArray(); for (int i = ccNumber.Length - 1; i >= 0; i--) { n = int.Parse(nx[i].ToString()); if (alternate) { n *= 2; if (n > 9) { n = (n % 10) + 1; } } sum += n; alternate = !alternate; } return (sum % 10 == 0); } Javascriptfunction checksum(value) { let d = value.split('') .map( (x) => parseInt(x) ) .map( (x,idx) => idx % 2 ? x * 3 : x ) .reduce( (accum, x) => accum += x ); d = d % 10; return d === 0 ? d : 10 - d; // Alternatively : return ( 10 - d % 10 ) % 10; } Pythondef luhn(purported): LUHN_ODD_LOOKUP = (0, 2, 4, 6, 8, 1, 3, 5, 7, 9) # sum_of_digits (index * 2) if not isinstance(purported, str): purported = str(purported) try: evens = sum(int(p) for p in purported[-1::-2]) odds = sum(LUHN_ODD_LOOKUP[int(p)] for p in purported[-2::-2]) return ((evens + odds) % 10 == 0) except ValueError: # Raised if an int conversion fails return False Swiftfunc calcCheckDigit( _ qr : String) -> String { var sum = 0 let reversedCharacters = qr.reversed().map { String($0) } for (var idx, element) in reversedCharacters.enumerated() { guard let digit = Int(element) else { return "" } idx += 1 switch (idx % 2 != 0) { case true : sum += digit > 4 ? ((digit * 2) % 10) + 1 : digit * 2 default: sum += digit } } let checkDigit = sum % 10 == 0 ? 0 : 10 - (sum % 10) return String(checkDigit) } func checkCreditCard(number: String) -> Bool { var sum = 0 var alternate = false number.reversed().forEach{ var n = Int("\\($0)") ?? 0 if alternate { n *= 2 if n > 9 { n = (n % 10) + 1 } } sum += n alternate = !alternate } return sum % 10 == 0 } //The above doesn't work //To calculate the Checkdigit try func MSICheckDigit (account:String) -> Int { var theSum = 0; var DoubleThis = true for character in account.reversed(){ if DoubleThis{ var thisDoubled:Int = (Int(String(character)) ?? 0) * 2 if thisDoubled > 9 { let AddThese:String = String(thisDoubled) var theNewDoubled:Int = 0; for character2 in AddThese{ theNewDoubled += Int(String(character2))! } thisDoubled = theNewDoubled } theSum += thisDoubled DoubleThis = false } else{ theSum += Int(String(character))! DoubleThis = true } } let theSumTimesNine:Int = theSum * 9 let theSumTimesNineString = String(theSumTimesNine) return Int(String(theSumTimesNineString.last!))! } Javapublic class Luhn {public static boolean check(String ccNumber) { int sum = 0; boolean alternate = false; for (int i = ccNumber.length() - 1; i >= 0; i--) { int n = Integer.parseInt(ccNumber.substring(i, i + 1)); if (alternate) { n *= 2; if (n > 9) { n = (n % 10) + 1; } } sum += n; alternate = !alternate; } return (sum % 10 == 0); } } Goimport "strconv" func luhn(number string) bool { var sum int64 var alternate bool for i := range number { n, err := strconv.ParseInt(number[i:i+1], 0, 64) if err != nil { return false } if alternate { n = n * 2 if n > 9 { n = (n % 10) + 1 } } alternate = !alternate sum = sum + n } return sum%10 == 0 } PeopleSoft&Char = &Number &Length = Len(&Char); &Char_1 = 0; &Char_2 = 0; &Char_3 = 0; &Char_4 = 0; For &i = 0 To &Length - 1 &Char_1 = Substring(&Char, &Length - &i, 1); If Mod(&i, 2) = 0 Then &Char_2 = &Char_1 * 2; If &Char_2 > 9 Then &Char_2 = &Char_2 - 9; End-If; Else &Char_2 = &Char_1; End-If; &Char_3 = &Char_3 + &Char_2; End-For; &Char_4 = Mod(&Char_3, 10); If &Char_4 <> 0 Then &Char_4 = 10 - &Char_4 Else &Char_4 = 0; End-If; &Final_Number = &Number | &Char_4; WinMessage(&Final_Number, 0); See also
References1. ^ISO/IEC 7812-1:2006 Identification cards -- Identification of issuers -- Part 1: Numbering system 2. ^US Patent 2,950,048 – Computer for Verifying Numbers, Hans P Luhn, August 23, 1960 External links
5 : Modular arithmetic|Checksum algorithms|Articles with example Python code|Error detection and correction|1954 introductions |
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