The Aadhaar number is made up of 12 digits. The first 11 digits are generated uniquely, while the final digit serves as a checksum.

The algorithm used for Aadhaar Number Validation is Verhoeff’s Algorithm,it was published by Dutch mathematician Jacobus Verhoeff in 1969.

Verhoeff’s Algorithm is a robust checksum-based error detection algorithm used to ensure the integrity and validity of numerical data, such as identification numbers. It is particularly effective against transcription and transposition errors, making it an ideal choice for verifying Aadhaar numbers.

Verhoeff’s Algorithm is a robust checksum-based error detection algorithm used to ensure the integrity and validity of numerical data, such as identification numbers. It is particularly effective against transcription and transposition errors, making it an ideal choice for verifying Aadhaar numbers.

Key Characteristics:

Error Detection: Verhoeff’s algorithm detects common human errors such as digit swaps (transpositions) and single-digit mistakes.
Mathematical Basis: The algorithm relies on modular arithmetic, permutations, and a special multiplication matrix.
Digit-by-Digit Validation: The algorithm processes each digit of a number in reverse order, ensuring that the entire number adheres to the checksum requirements.

Application in Aadhaar Numbers:

The Aadhaar number is a unique 12-digit identification number issued by the Indian government. Verhoeff’s algorithm is implemented to verify Aadhaar numbers for correctness by:

Ensuring no transcription or transposition errors occur during data entry.
Validating the structure and checksum of Aadhaar numbers before they are accepted by systems.

Benefits for Aadhaar Validation:

Accuracy: Prevents the entry of incorrect Aadhaar numbers into databases.
Efficiency: Provides a quick and systematic way to validate millions of Aadhaar numbers.
Security: Enhances trust in the Aadhaar identification system by reducing the chances of error or fraud.

C/C++

#include <stdio.h>
#include <string.h>
#include <ctype.h>

int isAadhaarValid(const char *aadhaarNo) {
if (aadhaarNo NULL || strlen(aadhaarNo) 0) {
return 0;
}
char sanitized[13];
int len = 0;
for (int i = 0; aadhaarNo[i] != '\0'; i++) {
if (isdigit(aadhaarNo[i])) {
sanitized[len++] = aadhaarNo[i];
}
}
sanitized[len] = '\0';
if (len != 12 || sanitized[0] < '2') {
return 0;
}
int multiplicationMatrix[10][10] = {
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
{1, 2, 3, 4, 0, 6, 7, 8, 9, 5},
{2, 3, 4, 0, 1, 7, 8, 9, 5, 6},
{3, 4, 0, 1, 2, 8, 9, 5, 6, 7},
{4, 0, 1, 2, 3, 9, 5, 6, 7, 8},
{5, 9, 8, 7, 6, 0, 4, 3, 2, 1},
{6, 5, 9, 8, 7, 1, 0, 4, 3, 2},
{7, 6, 5, 9, 8, 2, 1, 0, 4, 3},
{8, 7, 6, 5, 9, 3, 2, 1, 0, 4},
{9, 8, 7, 6, 5, 4, 3, 2, 1, 0}
};
int permutationMatrix[8][10] = {
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
{1, 5, 7, 6, 2, 8, 3, 0, 9, 4},
{5, 8, 0, 3, 7, 9, 6, 1, 4, 2},
{8, 9, 1, 6, 0, 4, 3, 5, 2, 7},
{9, 4, 5, 3, 1, 2, 6, 8, 7, 0},
{4, 2, 8, 6, 5, 7, 3, 9, 0, 1},
{2, 7, 9, 3, 8, 0, 6, 4, 1, 5},
{7, 0, 4, 6, 9, 1, 3, 2, 5, 8}
};
int checksum = 0;
for (int i = 0; i < 12; i++) {
int digit = sanitized[11 - i] - '0';
checksum = multiplicationMatrix[checksum][permutationMatrix[i % 8][digit]];
}
return checksum == 0;
}
int main() {
printf("%d\n", isAadhaarValid("YOUR_AADHAAR_CARD_NUMBER")); // Replace with real Aadhaar number
return 0;
}

Java

public class Main {
public static boolean isAadhaarValid(String aadhaarNo) {
if (aadhaarNo == null || aadhaarNo.isBlank()) {
return false;
}

int checksum = 0;
String sanitized = aadhaarNo.replace(" ", "").replace("-", "").replace("/", "");

if (sanitized.length() != 12) {
return false;
}

for (char c : sanitized.toCharArray()) {
if (!Character.isDigit(c)) {
return false;
}
}

if (sanitized.charAt(0) - '0' < 2) {
return false;
}

int[][] multiplicationMatrix = {
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
{1, 2, 3, 4, 0, 6, 7, 8, 9, 5},
{2, 3, 4, 0, 1, 7, 8, 9, 5, 6},
{3, 4, 0, 1, 2, 8, 9, 5, 6, 7},
{4, 0, 1, 2, 3, 9, 5, 6, 7, 8},
{5, 9, 8, 7, 6, 0, 4, 3, 2, 1},
{6, 5, 9, 8, 7, 1, 0, 4, 3, 2},
{7, 6, 5, 9, 8, 2, 1, 0, 4, 3},
{8, 7, 6, 5, 9, 3, 2, 1, 0, 4},
{9, 8, 7, 6, 5, 4, 3, 2, 1, 0}
};

int[][] permutationMatrix = {
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
{1, 5, 7, 6, 2, 8, 3, 0, 9, 4},
{5, 8, 0, 3, 7, 9, 6, 1, 4, 2},
{8, 9, 1, 6, 0, 4, 3, 5, 2, 7},
{9, 4, 5, 3, 1, 2, 6, 8, 7, 0},
{4, 2, 8, 6, 5, 7, 3, 9, 0, 1},
{2, 7, 9, 3, 8, 0, 6, 4, 1, 5},
{7, 0, 4, 6, 9, 1, 3, 2, 5, 8}
};

String reversed = new StringBuilder(sanitized).reverse().toString();

for (int i = 0; i < reversed.length(); i++) {
int digit = reversed.charAt(i) - '0';
checksum = multiplicationMatrix[checksum][permutationMatrix[i % 8][digit]];
}

return checksum == 0;
}

public static void main(String[] args) {
System.out.println(isAadhaarValid("YOUR_AADHAAR_CARD_NUMBER")); // Replace with real Aadhaar number
}
}

Kotlin

fun isAadhaarValid(aadhaarNo: String): Boolean
{
if (aadhaarNo.isBlank())
return false
var checksum = 0
aadhaarNo.replace(" ", "")
.replace("-", "").replace("/", "")
.apply {
if (length != 12)
return false
forEachIndexed { , c ->
if (!c.isDigit())
return false
}
if (first().toString().toInt() in 0..1)
return false

val multiplicationMatrix = arrayOf(
intArrayOf(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
intArrayOf(1, 2, 3, 4, 0, 6, 7, 8, 9, 5),
intArrayOf(2, 3, 4, 0, 1, 7, 8, 9, 5, 6),
intArrayOf(3, 4, 0, 1, 2, 8, 9, 5, 6, 7),
intArrayOf(4, 0, 1, 2, 3, 9, 5, 6, 7, 8),
intArrayOf(5, 9, 8, 7, 6, 0, 4, 3, 2, 1),
intArrayOf(6, 5, 9, 8, 7, 1, 0, 4, 3, 2),
intArrayOf(7, 6, 5, 9, 8, 2, 1, 0, 4, 3),
intArrayOf(8, 7, 6, 5, 9, 3, 2, 1, 0, 4),
intArrayOf(9, 8, 7, 6, 5, 4, 3, 2, 1, 0)
)
val permutationMatrix = arrayOf(
intArrayOf(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
intArrayOf(1, 5, 7, 6, 2, 8, 3, 0, 9, 4),
intArrayOf(5, 8, 0, 3, 7, 9, 6, 1, 4, 2),
intArrayOf(8, 9, 1, 6, 0, 4, 3, 5, 2, 7),
intArrayOf(9, 4, 5, 3, 1, 2, 6, 8, 7, 0),
intArrayOf(4, 2, 8, 6, 5, 7, 3, 9, 0, 1),
intArrayOf(2, 7, 9, 3, 8, 0, 6, 4, 1, 5),
intArrayOf(7, 0, 4, 6, 9, 1, 3, 2, 5, 8)
)

reversed().forEachIndexed { i, digit ->
checksum =
multiplicationMatrix[checksum][permutationMatrix[i % 8][digit.digitToInt()]]
}

}

return checksum 0
}

fun main() {
println(isAadhaarValid("YOURAADHAAR_CARD_NUMBER"))
} return checksum 0
}

Steps in the Algorithm:
1. Sanitization: Remove non-digit characters (e.g., spaces, hyphens) to ensure the input contains only numerical digits.
2. Reverse Digits: Process the number from the least significant digit to the most significant.
3. Checksum Calculation: For each digit, apply the multiplication matrix and the permutation table in sequence.
Combine the results to compute a cumulative checksum.
4. Validation: If the final checksum is 0, the number passes the validation.

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[Tutorial] How to Validate Aadhaar Card Number in C /C++ | Java | Kotlin.