DP Knapsack. Use table with columns 0 .. Capacity And rows 0 .. Number_objects. Table with several rows filled.

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DP Knapsack. Use table with columns 0 .. Capacity And rows 0 .. Number_objects. Table with several rows filled.

Knapsack Model. Intuitive idea: what is the most valuable collection of items that can be fit into a backpack?. Race Car Features. Budget of $35,000 Which features should be added?. Formulation. Decision variables ILP. LIN G O Formulation. MODEL : SETS :

Knapsack problem. There are two versions of the problem: (1) “0-1 knapsack problem” and (2) “Fractional knapsack problem” (1) Items are indivisible; you either take an item or not. Solved with dynamic programming

Knapsack Cryptosystems. Dinara Barshevich JASS’05 St. Petersburg. Brief historical background. 1976, Diffie & Hellman – Public Key Cryptosystem 1977 RSA – the first incarnation of such system 1978 Merkle – Hellman Cryptosystem 1980s years: attacks to MH. Agenda.

Knapsack Problem. A dynamic approach. Knapsack Problem. Given a sack, able to hold W kg Given a list of objects Each has a weight and a value Try to pack the object in the sack so that the total value is maximized. Variation. Rational Knapsack

Knapsack Cryptosystems. Behdad Esfahbod December 2001. Agenda. Knapsack problem and it ’ s computation complexity Knapsack as a public key cryptosystem The Merkle-Hellman knapsack cryptosystem Shamir ’ s attack to basic Merkle-Hellman Knapsack cryptosystem

Knapsack Model. Intuitive idea: what is the most valuable collection of items that can be fit into a backpack?. Race Car Features. Budget of $35,000 Which features should be added?. Formulation. Decision variables ILP. LIN G O Formulation. MODEL : SETS :

Knapsack Cryptosystems. Dinara Barshevich JASS’05 St. Petersburg. Brief historical background. 1976, Diffie & Hellman – Public Key Cryptosystem 1977 RSA – the first incarnation of such system 1978 Merkle – Hellman Cryptosystem 1980s years: attacks to MH. Agenda.

Approximate Knapsack. Get as much value as you can into the knapsack. Approximate Knapsack. Ingredients: Instances: The volume V of the knapsack. The volume and price of n objects <<v 1 ,p 1 >,<v 2 ,p 2 >,… ,<v n ,p n >>.