Verhoeff Algorithm - Strengths and Weaknesses

Strengths and Weaknesses

The Verhoeff algorithm will detect all occurrences of the following common transcription errors in a number:

• Replacement of a single digit by a different digit (a → b).
• Transposition (switching) of two adjacent digits (ab → ba).

Additionally, the Verhoeff algorithm detects most (but not all) occurrences of the following less common errors:

• Twin errors (aa → bb).
• Jump twin errors (aca → bcb).
• Jump transpositions (abc → cba).
• Phonetic errors (a0 ↔ 1a; e.g.; "sixty" ↔ "sixteen").

The main weakness of the Verhoeff algorithm is its complexity. Unlike the Luhn algorithm, the calculations required for a Verhoeff check digit cannot readily be performed by hand from memory.