How to validate a International Securities Identification Number (ISIN) number

Question

If I am not wrong, ISIN numbers last position is a verification digit. What is the mathematical function that determines its value in function of the first 11 digits?

Answer 1

I'd like to share my implementation in R. It does not require any specific package.

The mgsub is a support function that allows the substitution of all the characters in the ISIN code in one single command. It is copied from Replace multiple letters with accents with gsub

the iso3166alpha2$Code contains the list of countries that Grenade has listed

The algorithm is implemented in the isIsin(x) function, which returns TRUE in case of valid ISIN code

mgsub <- function(pattern, replacement, x, ...) {
  if (length(pattern)!=length(replacement)) {
    stop("pattern and replacement do not have the same length.")
  }
  result <- x
  for (i in 1:length(pattern)) {
    result <- gsub(pattern[i], replacement[i], result, ...)
  }
  result
}

isIsin <- function (identifier) {

  correctPrefix <- substr(identifier, 1, 2) %in% c(iso3166alpha2$Code, "XS")

  correctLength <- nchar(identifier) == 12  

  correctCharset <- !grepl('[[:punct:]]', identifier)

  if(!correctPrefix | !correctLength | !correctCharset) {
    return(FALSE)
  }

  # replace all character with its equivalent number  
  identifierOnlyNumbers <- mgsub(LETTERS, seq(10, 35), substr(identifier, 1, 11))

  # split the identifier in single digits and reverse its order
  characterVector <- rev(unlist(strsplit(identifierOnlyNumbers, "")))

  # Double every second digit of the group of digits with the rightmost character
  characterVector[seq(1, nchar(identifierOnlyNumbers), 2)] <- 
    as.character(as.numeric(characterVector[seq(1, nchar(identifierOnlyNumbers), 2)]) * 2)

  # Subtract 9 if > 9 (can apply to all since no digit can be greater than 9 before doubling)
  # Add up the digits
  summation <- sum(ifelse(as.numeric(characterVector) > 9, as.numeric(characterVector) - 9, as.numeric(characterVector)))

  # Take the 10s modulus of the sum, subtract it from 10 and take the 10s modulus of the result 
  # this final step is important in the instance where the modulus of the sum is 0, as the resulting check digit would be 10
  correctCheckDigit <- (10 - (summation %% 10)) %% 10 == as.numeric(substr(identifier, 12, 12))

  correctCheckDigit 

}