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Given f(x), it is easy to sample f'(x,Um) For any x, r, we can ... Use the inverter of f' to invert the output of Step 1. This outputs a (x', r') Output x' ...

A breaks f' DEC A breaks f. DEC uses A as a black box. could be ... A breaks f' DEC A breaks f. DEC uses A as a black box. Complexity. Transformation: ...

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From Any One-way Function Rafael Pass Cornell University Joint work with Huijia (Rachel) Lin

Not allowed: Directly access bit representations of F-elements ' ... Allowed operations: Add, subtract, multiply, or divide any two F-elements ...

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Closed captioning and other considerations provided by Tal Malkin, Luca Trevisan, ... Homomorphic. Encryption. UOWHFs. ID Based. Encryption. PIRs ...

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Generic and Practical Resettable Zero-Knowledge in the Bare Public-Key Model. Moti Yung ... The bare public-key (BPK) model. Concurrent verifier security in ...

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Commitment Schemes Hiding: A ... v21i, , hvm0, vm1 i To broadcast a single bit b to a subset T [m] Choose corresponding ... (Quantum computers?) New ...

Title: Concurrency and Non-malleability Author: Rafael Pass Last modified by: Rafael Pass Created Date: 9/6/2002 12:11:36 AM Document presentation format

On Constructing Parallel Pseudorandom Generators from One-Way Functions. Emanuele Viola ... Stretch s(n) 1 (e.g., s(n) = 1, s(n) = n) Fools efficient ...

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Hiding R does not learn x during the commit stage. ... 'One-way functions imply a 1-2 binding, statistically-hiding two-phase commitment' ...

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Semi-Honest to Malicious Oblivious-Transfer The Black-box Way Iftach Haitner Weizmann Institute of Science

High school diploma, School ? 15, Tallinn, 1993. M.Sc., Moscow State University, ... Is 3-Coloring hard on a random graph? likely to contain just say 'no' ...

g can be 'simpler' than f (meaning of 'simpler' determined by application) ... Correctness: f(x) can be efficiently decoded from g(x,r) ...

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rb must be non-repeating. Mutual authentication using random numbers ... Alice checks that ra, rb are the ones used earlier. Challenge-response authentication ...

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How to Use Indistinguishability Obfuscation Brent Waters Amit Sahai

Then the exponents ai can be determined by relationships among the prime factorizations ... m(M) = f(t) m(Mi)^ai. could be solved without factoring? Effective ...

Introduction to Modern Cryptography. Lecture 7. RSA Public Key CryptoSystem ... sure both (p-1), (q-1) have large prime factors (to foil Pollard's rho algorithm) ...

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Computers and 'Private key security' exist (DES), and are becoming more and more ... ( hush hush!) By 1976... ( biographical details) ...

COM 5336 Cryptography Lecture 6 Public Key Cryptography & RSA Scott CH Huang COM 5336 Cryptography Lecture 6 COM 5336 Cryptography Lecture 6 Scott CH Huang COM 5336 ...

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On the limitations of efficient computation Oded Goldreich Weizmann Institute of Science

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Examples: `physical implementations (noisy channel, quantum ... For all but bit commitment there is a direct construction of a combiner Example: ...

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r No shared secret between the origin and the recipient. no need to manage secret keys but integrity of K' must be assured with an off ...

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Oracle Workflow 12 Oracle ...

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Goal: try to simulate BPP is subexponential time (or better) ... Recall goal: for all 1 d 0, family of PRGs {Gm} with. output length m fooling size s = m ...

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