Mar 14 Midterm

# A Concrete Introduction to Higher Algebra, 2nd Edition

• Notes
• davidvictor
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University of California — Berkeley Handout CS276: Cryptography March 15, 2002 Professors Luca Trevisan and David Wagner Midterm This midterm is due at the start of class on Tuesday, March 19th. When you are asked to prove or disprove a statement S , you actually have three options: you may show that S is unconditionally true; you may show that S is unconditionally false; or, you may show that S is conditionally true under some standard assumption (e.g., that one-way functions exist) and false otherwise. For each problem, be sure to state clearly and precisely what result you are going to prove before proving it. You do not need to re-prove anything covered in class. This exam is “open-notes” (you may use anything in your notes or the online scribe notes) but “closed-book” (you may not use any textbook or other source). Problem 1. [Injective Pseudorandom Generators] We want to show that pseudorandom generators may or may not be 1-1 functions. (a) Assuming the existence of one-way permutations of superpolynomial security, prove the existence of a pseudorandom generator G : { 0 , 1 } n → { 0 , 1 } n +1 of superpolynomial security with the additional property that G is a 1-1 function.

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• Spring '02
• Trevisan
• Bitwise operation, one-way function, Pseudorandomness, elgamal encryption, pseudorandom generator

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