Towards realizing random oracles: Hash functions that hide all partial information

Securing Public Key Encryption Against Adaptive Chosen Ciphertext Attacks

Algorithmic Strategies for Solving Complex Problems in Cryptography - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-5225-2915-6.ch011 ◽

2018 ◽

pp. 134-144

Author(s):

Kannan Balasubramanian

Keyword(s):

Partial Information ◽

Hash Functions ◽

Public Key ◽

Public Key Encryption ◽

Public Key Cryptosystems ◽

Active Attacks ◽

Chosen Ciphertext Attack ◽

Decryption Oracle

To deal with active attacks in public key encryptions, the notion of security against an adaptive chosen ciphertext attack has been defined by Researchers. If an adversary can inject messages into a network, these messages may be ciphertexts, and the adversary may be able to extract partial information about the corresponding cleartexts through its interaction with parties in the network. The Security against chosen ciphertext attack is defined using an “decryption oracle.” Given an encryption of a message the “ciphertext” we want to guarantee that the adversary cannot obtain any partial information about the message. A method of securing Public Key Cryptosystems using hash functions is described in this chapter.

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On Pseudo-Random Oracles

Tatra Mountains Mathematical Publications ◽

10.2478/v10127-012-0045-5 ◽

2012 ◽

Vol 53 (1) ◽

pp. 155-187

Author(s):

Michal Rjaško

Keyword(s):

Hash Function ◽

Random Function ◽

Hash Functions ◽

Random Oracle Model ◽

Random Oracle ◽

Public Image ◽

Signature Schemes ◽

Random Oracles ◽

Random Behavior ◽

Domain Extension

ABSTRACT Many cryptographic systems which involve hash functions have proof of their security in a so called random oracle model. Behavior of hash functions used in such cryptographic systems should be as close as possible to the behavior of a random function. There are several properties of hash functions dealing with a random behavior. A hash function is pseudo-random oracle if it is indifferentiable from a random oracle. However, it is well known that hash functions based on the popular Merkle-Damg˚ard domain extension transform do not satisfy the pseudo-random oracle property. On the other hand no attack is known for many concrete applications utilizing Merkle-Damg˚ard hash functions. Hence, a weakened notion called public-use pseudo random oracle was introduced. The property can be met by the Merkle-Damg˚ard construction and is sufficient for several important applications. A hash function is public use pseudo-random oracle if it is indifferentiable from a random oracle with public messages (i.e., all messages hashed so far are available to all parties). This is the case of most hash based signature schemes. In this paper we analyze relationship between the property pseudo-random oracle and its variant public image pseudo-random oracle. Roughly, a hash function is public image pseudo-random oracle if it is indifferentiable from a random oracle with public images (i.e., all images of messages hashed so far are available to all parties, messages are kept secret). We prove that the properties are equivalent.

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