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New visual secret sharing schemes using probabilistic method

New visual secret sharing schemes using probabilistic method. Ching-Nung Yang Pattern Recognition Letters 25 , 2004 指導老師：李南逸 Speaker ：黃資真. Outline. Introduction ProbVSS scheme A k-out-of-n ProbVSS scheme A 2-out-of-2 ProbVSS scheme A 2-out-of-n ProbVSS scheme

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New visual secret sharing schemes using probabilistic method

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  1. New visual secret sharing schemes using probabilistic method Ching-Nung Yang Pattern Recognition Letters 25 , 2004 指導老師：李南逸 Speaker：黃資真

  2. Outline • Introduction • ProbVSS scheme • A k-out-of-n ProbVSS scheme • A 2-out-of-2 ProbVSS scheme • A 2-out-of-n ProbVSS scheme • A k-out-of-k ProbVSS scheme • A general k-out-of-n ProbVSS scheme • Conclusion

  3. Introduction • White pixels show the contrast of recovered image. • The new scheme is non-expansible shadow.

  4. ProbVSS scheme Probabilistic scheme use the abbreviation ProbVSS scheme.

  5. A k-out-of-n ProbVSS scheme • A (k,n) ProbVSS Scheme is conditions ： • n*1 matrices in the set and , L(V) operation values of all matrices form two sets λ and γ. • The two sets λ and γ satisfy that ≧ and ≦ -α. • For any subset { } of {1,2,…,n} with q<k, the and are the same.

  6. Construction： Theorem： Proof. A 2-out-of-2 ProbVSS scheme

  7. A 2-out-of-2 ProbVSS scheme • Proof of third condition “security”： • Shadow 1 λ={L([0]) , L([1])} = {0,1} , =0.5 γ={L([0]) , L([1])} = {0,1} , =0.5 • Shadow 2 λ={L([0]) , L([1])} = {0,1}, =0.5 γ={L([1]) , L([0])} = {1,0}, =0.5

  8. A 2-out-of-n ProbVSS scheme Construction 1： Theorem 1：

  9. A 2-out-of-n ProbVSS scheme • Proof：　A (2,3) ProbVSS scheme

  10. A 2-out-of-n ProbVSS scheme • Proof：　A (2,4) ProbVSS scheme

  11. Construction 2： Theorem 2： A 2-out-of-n ProbVSS scheme

  12. A 2-out-of-n ProbVSS scheme • Proof：　A (2,3) ProbVSS scheme

  13. A k-out-of-k ProbVSS scheme • Construction 2： • Theorem 2：

  14. A k-out-of-k ProbVSS scheme • Proof：　A (3,3) ProbVSS scheme

  15. A general k-out-of-n ProbVSS scheme

  16. A general k-out-of-n ProbVSS scheme • Construction : • Theorem：

  17. Proof： A Shamir’s (3,4) VSS scheme with white and black matrices A general k-out-of-n ProbVSS scheme

  18. Conclusion • New (k,n) ProbVSS schemes with non-expansible shadow size based on the probabilistic method. • The conventional VSS scheme can be transferred to ProbVSS scheme. • The ProbVSS scheme is a different view of the conventional VSS scheme.

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