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TCS Forum the 9th of November 2007

Professor Jorma Jormakka PhD in Mathematics University of Helsinki 2000 - 2004 Professor, Networking laboratory, Department of Electrical Engineering, TKK 2000 Professor, National Defence University On existence of polynomial-time algorithms for the Merkle-Hellman knapsack problem.

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TCS Forum the 9th of November 2007

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  1. Professor Jorma Jormakka PhD in Mathematics University of Helsinki 2000 - 2004 Professor, Networking laboratory, Department of Electrical Engineering, TKK 2000 Professor, National Defence University On existence of polynomial-time algorithms for the Merkle-Hellman knapsack problem TCS Forum the 9th of November 2007

  2. Merkle-Hellman Knapsack Cryptosystem • An asymmetric-key cryptosystem • Unlike RSA, the public key is used only for encryption, and the private key is used only for decryption. • The Merkle-Hellman system is based on the subset sum problem: given a list of numbers and a third number, which is the sum of a subset of these numbers, determine the subset. • Subset sum problem is known to be NP-complete. • If the set of numbers is super-increasing, that is, each element of the set is greater than the sum of all the numbers before it, the problem is 'easy' and solvable in polynomial time with a simple greedy algorithm. • Private key is composed of a super-increasing set of numbers, and a multiplier and a modulus, which are used to convert the easy subset sum problem to a difficult one. • Public key is the difficult subset sum problem.

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