A Latin square autotopism secret sharing scheme Talk by Rebecca J. - PowerPoint PPT Presentation

A Latin square autotopism secret sharing scheme Talk by Rebecca J. Stones Co-authors: Ming Su, Xiaoguang Liu, Gang Wang, (Nankai University) and Sheng Lin (Tianjin University of Technology). September 12, 2014

Secret sharing schemes Secret sharing schemes describe how to distribute pieces of information, called shares , among participants so that:

Secret sharing schemes Secret sharing schemes describe how to distribute pieces of information, called shares , among participants so that: if the participants cooperate, their collective shares can be used to recover a secret message, and

Secret sharing schemes Secret sharing schemes describe how to distribute pieces of information, called shares , among participants so that: if the participants cooperate, their collective shares can be used to recover a secret message, and if too few participants cooperate, then the secret cannot be recovered.

A toy example... share 1 share 2 � ��     1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0     1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0          0 0 1 0 0 1 0 1 1 0   0 1 1 1 0 1 0 0 1 0          1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0          0 1 1 1 0 0 0 0 1 1   1 1 1 0 0 0 0 0 1 0          0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0             1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0          0 1 1 1 0 0 0 0 1 0   0 1 0 1 0 1 0 0 1 1          1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0     1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1

A toy example... share 1 share 2 addition modulo 2 reveals secret � ��       1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0       1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0              0 0 1 0 0 1 0 1 1 0   0 1 1 1 0 1 0 0 1 0   0 1 0 1 0 0 0 1 0 0              1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0                 0 1 1 1 0 0 0 0 1 1  1 1 1 0 0 0 0 0 1 0  1 0 0 1 0 0 0 0 0 1       + =       0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0                   1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1             0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1                   1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0       1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0

A toy example... share 1 share 2 addition modulo 2 reveals secret � ��       1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0       1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0              0 0 1 0 0 1 0 1 1 0   0 1 1 1 0 1 0 0 1 0   0 1 0 1 0 0 0 1 0 0              1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0                 0 1 1 1 0 0 0 0 1 1  1 1 1 0 0 0 0 0 1 0  1 0 0 1 0 0 0 0 0 1       + =       0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0                   1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1             0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1                   1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0       1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 We can’t find the secret without both shares.

A toy example... share 1 share 2 addition modulo 2 reveals secret � ��       1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0       1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0              0 0 1 0 0 1 0 1 1 0   0 1 1 1 0 1 0 0 1 0   0 1 0 1 0 0 0 1 0 0              1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0                 0 1 1 1 0 0 0 0 1 1  1 1 1 0 0 0 0 0 1 0  1 0 0 1 0 0 0 0 0 1       + =       0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0                   1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1             0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1                   1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0       1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 We can’t find the secret without both shares. We can choose share 1 uniformly at random.

A toy example... share 1 share 2 addition modulo 2 reveals secret � ��       1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0       1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0              0 0 1 0 0 1 0 1 1 0   0 1 1 1 0 1 0 0 1 0   0 1 0 1 0 0 0 1 0 0              1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0                 0 1 1 1 0 0 0 0 1 1  1 1 1 0 0 0 0 0 1 0  1 0 0 1 0 0 0 0 0 1       + =       0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0                   1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1             0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1                   1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0       1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 We can’t find the secret without both shares. We can choose share 1 uniformly at random. And choose share 2 to so that “share 1 + share 2” reveals the secret.

Shamir’s Secret Sharing Scheme Adi Shamir (of RSA fame) developed a secret sharing scheme. ( How to share a secret (1979), Comm. ACM.)

Shamir’s Secret Sharing Scheme Adi Shamir (of RSA fame) developed a secret sharing scheme. ( How to share a secret (1979), Comm. ACM.) We have ℓ participants,

Shamir’s Secret Sharing Scheme Adi Shamir (of RSA fame) developed a secret sharing scheme. ( How to share a secret (1979), Comm. ACM.) We have ℓ participants, a secret number c , and

Shamir’s Secret Sharing Scheme Adi Shamir (of RSA fame) developed a secret sharing scheme. ( How to share a secret (1979), Comm. ACM.) We have ℓ participants, a secret number c , and we want any t of the participants to be able to recover the secret.

A Latin square autotopism secret sharing scheme Talk by Rebecca J. - PowerPoint PPT Presentation

A Latin square autotopism secret sharing scheme Talk by Rebecca J. Stones Co-authors: Ming Su, Xiaoguang Liu, Gang Wang, (Nankai University) and Sheng Lin (Tianjin University of Technology). September 12, 2014 Secret sharing schemes Secret

Secret Sharing and Visual Cryptography Outline Secret Sharing Visual Secret Sharing

Vector Space Secret Sharing Scheme Mustafa Atici Western Kentucky University Department of

Homomorphic Secret Sharing for Low Degree Polynomials Russell W. F. Lai, Giulio Malavolta , and

Advanced Tools from Modern Cryptography Lecture 3 Secret-Sharing (ctd.) Secret-Sharing Last

Computing autotopism groups of partial Latin rectangles: a pilot study Ra ul M. Falc on (U.

Totally Symmetric Partial Latin Squares with Trivial Autotopism Groups Trent G. Marbach

Homomorphic Secret Sharing II Homomorphic Secret Sharing for Branching Programs Under DDH Ele:e

Protecting AES with Shamirs Secret Sharing Scheme Louis Goubin and Ange Martinelli CHES 2011,

Secret Sharing See: Shamir, How to Share a Secret , CACM, Vol. 22, No. 11, November 1979, pp.

Breaking the Circuit-Size Barrier in Secret Sharing Tianren Liu Vinod Vaikuntanathan MIT MIT

Secret Sharing Using Non-Commutative Groups Bren Cavallo The Graduate Center, CUNY 5/30/2013

Today. Polynomials. Secret Sharing. A secret! I have a secret! A number from 0 to 10. What is

Towards Breaking the Exponential Barrier for General Secret Sharing Tianren Liu Vinod

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1 f x y z T C V M H G Q D O N U X E R W P B A L I S F J K Y Z z M T N Z J K A

Securing Secret Sharing Against Leakage and Tampering Ashutosh Kumar Based on joint works with

Latin square determinants and permanents Ken Johnson Penn State Abington College (Joint work

Berkeley CS276 & MIT 6.875 Secret sharing and applications Lecturer: Raluca Ada Popa

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Searching for Doubly Self Searching for Doubly Self- Orthogonal Latin Squares Orthogonal Latin

Efficient Leakage-Resilient Secret Sharing Peihan Miao Akshayaram Srinivasan Prashant Nalini

Group embeddings of partial Latin squares Ian Wanless Monash University Latin squares Latin

escrypt GmbH for Embedded Security A Generic Architecture and Extension of eCryptfs: Secret

A Latin square autotopism secret sharing scheme Talk by Rebecca J. - PowerPoint PPT Presentation

A Latin square autotopism secret sharing scheme Talk by Rebecca J. Stones Co-authors: Ming Su, Xiaoguang Liu, Gang Wang, (Nankai University) and Sheng Lin (Tianjin University of Technology). September 12, 2014 Secret sharing schemes Secret

Secret Sharing and Visual Cryptography Outline Secret Sharing Visual Secret Sharing

Vector Space Secret Sharing Scheme Mustafa Atici Western Kentucky University Department of

Homomorphic Secret Sharing for Low Degree Polynomials Russell W. F. Lai, Giulio Malavolta , and

Advanced Tools from Modern Cryptography Lecture 3 Secret-Sharing (ctd.) Secret-Sharing Last

Computing autotopism groups of partial Latin rectangles: a pilot study Ra ul M. Falc on (U.

Totally Symmetric Partial Latin Squares with Trivial Autotopism Groups Trent G. Marbach

Homomorphic Secret Sharing II Homomorphic Secret Sharing for Branching Programs Under DDH Ele:e

Protecting AES with Shamirs Secret Sharing Scheme Louis Goubin and Ange Martinelli CHES 2011,

Secret Sharing See: Shamir, How to Share a Secret , CACM, Vol. 22, No. 11, November 1979, pp.

Breaking the Circuit-Size Barrier in Secret Sharing Tianren Liu Vinod Vaikuntanathan MIT MIT

Secret Sharing Using Non-Commutative Groups Bren Cavallo The Graduate Center, CUNY 5/30/2013

Today. Polynomials. Secret Sharing. A secret! I have a secret! A number from 0 to 10. What is

Towards Breaking the Exponential Barrier for General Secret Sharing Tianren Liu Vinod

CS 166: Information Security Secret Sharing, Random Numbers, and Information Hiding Prof. Tom

On the Local Leakage Resilience of Linear Secret Sharing Schemes Linear Secret Sharing Schemes

1 f x y z T C V M H G Q D O N U X E R W P B A L I S F J K Y Z z M T N Z J K A

Securing Secret Sharing Against Leakage and Tampering Ashutosh Kumar Based on joint works with

Latin square determinants and permanents Ken Johnson Penn State Abington College (Joint work

Berkeley CS276 &amp; MIT 6.875 Secret sharing and applications Lecturer: Raluca Ada Popa

Today. Secret Sharing. Polynomials A polynomial P ( x ) = a d x d + a d 1 x d 1 +

Searching for Doubly Self Searching for Doubly Self- Orthogonal Latin Squares Orthogonal Latin

Efficient Leakage-Resilient Secret Sharing Peihan Miao Akshayaram Srinivasan Prashant Nalini

Group embeddings of partial Latin squares Ian Wanless Monash University Latin squares Latin

escrypt GmbH for Embedded Security A Generic Architecture and Extension of eCryptfs: Secret

Berkeley CS276 & MIT 6.875 Secret sharing and applications Lecturer: Raluca Ada Popa