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Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai [1] who presented a family of one-way functions based on SIS problem.
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices.The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic ...
In 1996, Miklós Ajtai introduced the first lattice-based cryptographic construction whose security could be based on the hardness of well-studied lattice problems, [3] and Cynthia Dwork showed that a certain average-case lattice problem, known as short integer solutions (SIS), is at least as hard to solve as a worst-case lattice problem. [4]
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In 1999, Nguyen [1] showed that the GGH encryption scheme has a flaw in the design. He showed that every ciphertext reveals information about the plaintext and that the problem of decryption could be turned into a special closest vector problem much easier to solve than the general CVP.
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In cryptography, an initialization vector (IV) or starting variable [1] is an input to a cryptographic primitive being used to provide the initial state. The IV is typically required to be random or pseudorandom , but sometimes an IV only needs to be unpredictable or unique.
A major goal in cryptography is to create cryptographic primitives with provable security. In some cases, cryptographic protocols are found to have information theoretic security; the one-time pad is a common example. However, information theoretic security cannot always be achieved; in such cases, cryptographers fall back to computational ...