Aadhaar Card Masker & Redactor (2025/2026 UIDAI Privacy Compliance)

Mathematical Derivation & Variable Explanations: The 12-digit Aadhaar number is mathematically masked while preserving cryptographic and physical verification capabilities.

• Standard Masked Aadhaar Redaction Pattern:
  $$\text{Masked Aadhaar} = \underbrace{\text{XXXX}}_{\text{Digits 1–4}} - \underbrace{\text{XXXX}}_{\text{Digits 5–8}} - \underbrace{D_9 D_{10} D_{11} D_{12}}_{\text{Visible Last 4 Digits}}$$
  The first 8 numerical digits are permanently redacted or overwritten with optical black bounding boxes. Only the last 4 digits ($D_9 D_{10} D_{11} D_{12}$) remain visible to cross-reference identity documents.
• Verhoeff Dihedral Group $D_5$ Checksum Architecture:
  $$\sum_{i=0}^{11} d\left(c_i, \ p(i, a_i)\right) = 0$$
  The full 12-digit Aadhaar number incorporates the Verhoeff error detection checksum based on the non-commutative dihedral group of order 10 ($D_5$). Redacting the first 8 digits prevents third parties from reverse-engineering the underlying checksum or cloning biometric credentials.
• Offline Secure QR Code Verification (RSA 2048-Bit Signature): Masked Aadhaar cards issued by UIDAI retain the 2D secure QR code. The QR code contains an immutable RSA 2048-bit digital signature from UIDAI, allowing offline verifiers (airports, banks) to authenticate the cardholder's photograph, name, gender, and address without accessing central UIDAI biometric databases.
• Verhoeff Dihedral Group $D_5$ Matrix Operations: The Verhoeff algorithm utilizes the symmetries of a regular pentagon (the non-commutative group $D_5$ of order 10) through two fixed tables: multiplication table $d(j, k)$ and permutation table $p(i, j)$. For a 12-digit Aadhaar number $a_{11} a_{10} \dots a_0$, the validation condition is:
  $$c = \sum_{i=0}^{11} d\left( c, p\left( i \bmod 8, a_i \right) \right) = 0$$
  This mathematical formulation detects 100% of single-digit transcription errors and 100% of adjacent transposition errors.
• HTML5 Canvas 2D Irreversible Bounding Box Redaction: When a user highlights or an automated client OCR detects the bounding box $[x_0, y_0, w, h]$ encompassing the first 8 digits, our in-browser engine calls ctx.fillRect(x_0 - 2, y_0 - 2, w + 4, h + 4) with solid RGB black $(0, 0, 0, 1.0)$. This physically overwrites the underlying pixel array in local memory, permanently destroying original pixel values and text glyph vectors prior to file export.
• Penal Provisions under Section 42 & 43 of the Aadhaar Act: Demanding or storing unmasked physical Aadhaar cards without statutory authorization attracts imprisonment up to 3 years and financial penalties up to ₹10,000 per violation.