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Modulo-11

Modulo-11 weighted checksum used in ISBN-10, ISSN, and various identification systems. Uses position-based weights to detect single-digit errors and most transposition errors. Check digit can be 0-9 or X (representing 10).

Properties

Property	Value
Category	Checksums
Sub-category	Modular Arithmetic
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	ISBN/ISSN standard
Year	1970
Origin	Not specified
Source	`algorithms/checksum/modulo.js`

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Notes

Algorithm: weighted sum with position-based weights
Standard weights: (n+1), n, (n-1), …, 2 from LEFT to RIGHT
For ISBN-10 (9 digits): weights are 10, 9, 8, 7, 6, 5, 4, 3, 2
Check digit: (11 - sum mod 11) mod 11
Result 10 represented as ‘X’ in ISBN
Used in: ISBN-10, ISSN, bank routing numbers
Detects: All single-digit errors
Detects: Most adjacent transposition errors
Output: 0-9 or 10 (for ‘X’)

Documentation

References

python-stdnum ISBN-10 modulo-11 check digit implementation

Test vectors

3 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — ISBN-10 format

Field	Value
`input`	`303132303030303038`
`expected`	`03`

Vector 2 — Simple digit sequence

Source: Modulo-11 weighted checksum

Field	Value
`input`	`313233343536373839`
`expected`	`0a`

Vector 3 — Zero digits

Source: Modulo-11 edge case

Field	Value
`input`	`3030`
`expected`	`00`

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