PPT-Protecting Obfuscation Against Algebraic Attacks

Boaz Barak Sanjam Garg Yael Tauman Kalai Omer Paneth Amit Sahai Program Obfuscation Public Key     Obfuscation       Virtual BlackBox VBB Barak Goldreich . Unlock stories by generalising . number properties. ANDREW WILES. Why is this man so famous?. Fermat’s last theorem. No positive . integers satisfy the equation:. . n > 2.  . On doing mathematics…. Goal: Use problem solving strategies to solve real-life problems.. Definitions. :. Verbal Model. : the equation written in words.. Algebraic Model. : a mathematical statement written from a verbal model.. Evasive Functions. Boaz . Barak, . Nir. . Bitansky. , Ran Canetti,. Yael Tauman . Kalai, . Omer . Paneth, . Amit Sahai. Program Obfuscation . Obfuscated Program. Approved . Document . Signature . Obfuscation. Nir. . Bitansky. and Omer . Paneth. Program Obfuscation. Compute .  .  .  . Program Obfuscation.  .  . Program Obfuscation. Sign email . with . If . starts with “omer@bu.edu”.  .  .  . Zhicong Huang, Erman Ayday, Jacques Fellay, Jean-Pierre Hubaux, Ari Juels. Presented by Chuong Ngo. The Genomic Future. The Genomic Future. The Genomic Future. The Genomic Future. The Genomic Future. Unit 7 – Writing Algebraic Expressions with Addition and Subtraction. Vocabulary. Expressions. - A mathematical representation containing numbers, variables, and operation symbols; an expression does not include an equality or inequality symbol.. Translate each into an algebraic expression:. Two more than a number. . n. = number. 2+n. Translate each into an algebraic expression:. Two less than a number. n. = the number. n. -2. Translate each into an algebraic expression:. Representations . and . Proof. Learning Focus. Participants will:. deepen mathematical content knowledge of algebraic reasoning. develop awareness of key concepts associated with algebraic reasoning, . Boaz . Barak, . Nir. . Bitansky. , Ran Canetti,. Yael Tauman . Kalai, . Omer . Paneth, . Amit Sahai. Program Obfuscation . Obfuscated Program. Approved . Document . Signature . Obfuscation. Verify and sign. Nir. . Bitansky. and Omer . Paneth. Program Obfuscation. Compute .  .  .  . Program Obfuscation.  .  . Program Obfuscation. Sign email . with . If . starts with “omer@bu.edu”.  .  .  . Goyal. . Venkata. . Koppula. Brent Waters. Lockable Obfuscation. . . Correctness: . Challenger. Attacker. Lockable . Obfuscation: Security. OR. Guess. could . be from . high . entropy . dist.  . Contact: . Ibéria. Medeiros, Nuno . Neves. {. imedeiros. , nuno}@. di.fc.ul.pt. . FCiências.ID / LASIGE, . Faculdade. de . Ciências. , . Universidade. de . Lisboa. www.navigators.di.fc.ul.pt. Databases continue to be the most commonly used backend storage in enterprises, and are employed in several contexts in the electrical grid. They are often integrated with vulnerable applications, such as web frontends, that allow injection attacks to be performed. The effectiveness of such attacks steams from a . Essential Question: How can you simplify an algebraic expression?. 7. X + . 10 . . Coefficient. Variable. Constant. Like terms: Rules:. Same Variable . AND. same exponent. Coefficients can be different (# attached to variable). Sanjam. . Garg. , Craig Gentry*, . Shai Halevi*. ,. Mariana . Raykova. , . Amit. . Sahai. , Brent Waters. Faces in Modern Cryptography, Oct-2013. A Celebration in Honor of . . Goldwasser. . and .