AbstractInthispaper,weproposeamethodsuchthatasecretimageissharedbyn shadowimages,andanyr shadowimages(rpn)ofthemcanbeusedtorestorethewholesecretimage.Thesizeofeachshadowimageissmallerthanthesecretimageinourmethod.Thispropertygivesthebenefitinfurtherprocessoftheshadowimages,suchasstorage,transmission,orimagehiding.r 2002ElsevierScienceLtd.Allrightsreserved. Keywords: Secretsharing;Losslessreveal;Shadowimages;Grayvaluerange 1. IntroductionSecrettextsandimagesoftenexistinthecommercialormilitaryapplication.Aboutthestorageofthesecretdataorimages,thesecurityisofbigconcern.Inrecentyears,manytechniquestoincreasethesecurityofthesecret were proposed; examples include image hidingandwatermarking.However,acommonweaknessofthesetechniquesisthatthesecretdataareallinasingleinformation-carrier, and the secret data cannot berevealedcompletelyiftheinformation-carrierislostorcrippled. If we use many duplicates to overcome theweakness, the danger of security exposure will alsoincrease.Tosolvethisdilemma,secretsharingmethodmightbeoneofthepossiblesolutions.Blakley [1] and Shamir [2] first independently pro-posedtheconceptofsecretsharing.Itwascalledthe(r;n) threshold scheme. The succeeding studies weremainlyrelatedtothesecurityofthekeys[3–6].Whenthesecretdataareinfactsecretimages,becausethenumberofbytesusedinadigitalimageisusuallyverylarge(forexample,512 512)andthegrayvalueisbounded(0–255),usingthe(r;n)thresholdschemedirectlywillwastealotofmemoryspace;weshouldthereforedevelopaspecificmethodforsecretimagesharing.Inthispaper,weproposeasecretimagesharingmethodderivedfromthe(r;n)thresholdscheme.Inourmethod,thesizeofeachshadowimagewillbesmallerthanthatofthesecretimage,aswillbeseenlater.Wewillrequirethat:1. The secret image is used to generate n shadowimages.2. Any r or more shadow images can be used toreconstructthesecretimage.3. Anyr 1orlessshadowimagescannotgetsufficientinformationtorevealthesecretimage.Intherestofthispaper,the(r;n)thresholdschemeisreviewedinSection2.Section3introducesoursecretsharing method. The experimental result is shown inSection4.InSection5,weprovidethesecurityanalysis.ThebenefitsofthesizereductionoftheshadowimagesarediscussedinSection6.Finally,theconclusionsarestatedinSection7.2. The(r;n)thresholdscheme:areviewBecauseourmethodisbasedonthe(r;n)thresholdschemeproposedbyShamir,weroughlyintroducehisschemefirst.SupposethatwewanttodividethesecretdataD inton shadows(D
[1]
Douglas R. Stinson,et al.
Decomposition constructions for secret-sharing schemes
,
1994,
IEEE Trans. Inf. Theory.
[2]
W. Tsai,et al.
Spatial-domain image hiding using image differencing
,
2000
.
[3]
G. R. BLAKLEY.
Safeguarding cryptographic keys
,
1979,
1979 International Workshop on Managing Requirements Knowledge (MARK).
[4]
Amos Beimel,et al.
Secret Sharing With Public Reconstruction
,
1998
.
[5]
Amos Beimel,et al.
Universally ideal secret-sharing schemes
,
1994,
IEEE Trans. Inf. Theory.
[6]
Adi Shamir,et al.
How to share a secret
,
1979,
CACM.
[7]
B. S. Manjunath,et al.
A robust data hiding technique using multidimensional lattices
,
1998,
Proceedings IEEE International Forum on Research and Technology Advances in Digital Libraries -ADL'98-.
[8]
Rudolf Ahlswede,et al.
Common randomness in information theory and cryptography - I: Secret sharing
,
1993,
IEEE Trans. Inf. Theory.
[9]
Nasir D. Memon,et al.
Steganalysis of watermarking techniques using image quality metrics
,
2001,
IS&T/SPIE Electronic Imaging.