PPT-Merkle-Hellman Knapsack Cryptosystem

Merkle offered 100 award for breaking singly iterated knapsack Singlyiterated Merkle Hellman KC was broken by Adi Shamir in 1982   At the CRYPTO 83 conference Adleman used an Apple II computer to demonstrate Shamirs method . eXternalDie-Hellman(XDH)Assumption.XDHstatesthattheDeci-sionalDie-Hellman(DDH)problemishardinG1,implyingthattheisomor-phism isone-way.2q-DecisionalDie-HellmanInversion(DBDHI)Assumption.DBDHIasserts System. with . Efficient Integrity Checks. Marten van. . Dijk. Ari . Juels. Alina. . Oprea. RSA Labs. RSA Labs. RSA Labs. marten.vandijk@rsa.com. ari.juels@rsa.com. alina.oprea@rsa.com. Emil Stefanov. By. Farnoosh Davoodi. 1. Agenda. Min Knapsack Problem. 2 approximation greedy algorithm. Proof . 3/2 approximation greedy algorithm. Proof. Another improved heuristic. Heuristics for the O-1 Min-Knapsack Problem. A dynamic approach. Knapsack Problem. Given a sack, able to hold K 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. 1. Tsvi. . Kopelowitz. Knapsack. Given: a set S of n objects with weights and values, and a weight bound:. w. 1. , w. 2. , …, w. n. , B (weights, weight bound).. v. 1. , v. 2. , …, v. n. (values - profit).. Merkle offered $100 award for breaking singly - iterated knapsack. Singly-iterated Merkle - Hellman KC was broken by Adi Shamir in 1982   . At the CRYPTO ’83 conference, Adleman used an Apple II computer to demonstrate Shamir’s method . Sophia Yakoubov. Joint work with Leo . Reyzin. 1. Outline. Motivation: Distributed PKI. Background: Accumulators. Our Contributions: Asynchronous Accumulators. Definition: verification works even if the accumulator and witness are out of synch. and. Given positive integers v. i. and . w. i. for . i = 1, 2, ..., n.. and positive integers. K . and. W.. Does there exist a subset . S . of. {1, 2, ..., n}. such that:. A special case: S. UBSET. Definisi. Kriptografi. (. atau. . kriptologi. ; . dari. . bahasa. . Yunani. . κρυπτός . kryptós. , ". tersembunyi. , . rahasia. "; . dan. . γράφειν . graphein. , ". menulis. ", . & . ECC Diffie-Hellman. Presenter. : Le . Thanh. . Binh. Outline. What is . Elliptic Curve ?. Addition on an elliptic curve. Elliptic Curve Crypto (ECC). ECC Diffie–Hellman . Lets start with a puzzle…. 1. Dynamic Programming: . 0/1 Knapsack. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. Dynamic Programming. 2. The 0/1 Knapsack Problem. Blum-. Goldwasser. Cryptosystem. b. y . Yernar. Background. Key generation. Encryption. Decryption. Preset Bits. Example. Rabin Cryptosystem. Asymmetric cryptographic technique, whose security, like that of RSA, is related to the difficulty of factorization.. Part 5. Summary created by. Kirk Scott. 1. This set of overheads corresponds to . the first . portion of section 12.3 in the book. The overheads for Chapter 12 roughly track the topics in the chapter. Outline. Knapsack revisited: How to output the optimal solution, and how to prove correctness?. Longest Common Subsequence. Maximum Independent Set on Trees.. Example 2 Knapsack Problem. There is a knapsack that can hold items of total weight at most .