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The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, 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 US, and Canadian Social Insurance Numbers. 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.〔(ISO/IEC 7812-1:2006 Identification cards -- Identification of issuers -- Part 1: Numbering system )〕 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. ==Description== The 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: # From the rightmost digit, which is the check digit, moving left, double the value of every second digit; if the product of this doubling operation is greater than 9 (e.g., 8 × 2 = 16), then sum the digits of the products (e.g., 16: 1 + 6 = 7, 18: 1 + 8 = 9). # Take the sum of all the digits. # If the total modulo 10 is equal to 0 (if the total ends in zero) then the number is valid according to the Luhn formula; else it is not valid. 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: # Compute the sum of the non-check digits (67). # Multiply by 9 (603). # The last digit, 3, is the check digit. Thus, x=3. (Alternative method) The check digit (x) is obtained by computing the sum of the other digits then subtracting the units digit from 10 (67 => Units digit 7; 10 − 7 = check digit 3). In algorithm form: # Compute the sum of the digits (67). # Take the units digit (7). # Subtract the units digit from 10. # The result (3) is the check digit. In case the sum of digits ends in 0, 0 is the check digit. 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. #Double every second digit, from the rightmost: (1×2) = 2, (8×2) = 16, (3×2) = 6, (2×2) = 4, (9×2) = 18 #Sum all the ''individual'' digits (digits in parentheses are the products from Step 1): x (the check digit) + (2) + 7 + (1+6) + 9 + (6) + 7 + (4) + 9 + (1+8) + 7 = x + 67. #If the sum is a multiple of 10, the account number is possibly valid. Note that 3 is the only valid digit that produces a sum (70) that is a multiple of 10. #Thus these account numbers are all invalid except possibly 79927398713 which has the correct check digit. Alternately (if you don't want to confuse yourself by performing an algorithm on the whole number including the checksum digit), you can use the same checksum creation algorithm (mentioned a couple paragraphs up), ignoring the checksum already in place, as if it had not yet been calculated, and now you were calculating it for the first time. 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Luhn algorithm」の詳細全文を読む スポンサード リンク
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