We study notions and schemes for symmetric ie. private key encryption in a concrete security framework.We give four di erent notions of security against chosen plaintext attack and analyze the concrete complexity o f reductions among them, providing both upper and lower bounds, and obtaining tight relations. In this way w e classify notions even though polynomially reducible to each other as stronger or weaker in terms of concrete security.Next we provide concrete security analyses of methods to encrypt using a block cipher, including the most popular encryption method, CBC. We establish tight bounds meaning matching upper bounds and attacks on the success of adversaries as a function of their resources.

Abstract. We compare the relative strengths of popular notions of security for public key encryption schemes. We consider the goals of privacy and non-malleability, each under chosen plaintext attack and two kinds of chosen ciphertext attack. For each of the resulting pairs of definitions we prove either an implication (every scheme meeting one no~ion must meet the other) or a separation (there is a scheme meeting one notion but not the other, assuming the first notion can be met at all). We similaxly treat plaintext awareness, a notion of security in the random oracle model. An additional contribution of this paper is a new definition of non-malleability which we believe is simpler than the previous one.

We consider a novel security requirement of encryption schemes that we call "key-privacy" or "anonymity". It asks that an eavesdropper in possession of a ciphertext not be able to tell which specific key, out of a set of known public keys, is the one under which the ciphertext was created, meaning the receiver is anonymous from the point of view of the adversary. We investigate the anonymity of known encryption schemes. We prove that the El Gamal scheme provides anonymity under chosen-plaintext attack assuming the Decision Diffie-Hellman problem is hard and that the Cramer-Shoup scheme provides anonymity under chosen-ciphertext attack under the same assumption. We also consider anonymity for trapdoor permutations. Known attacks indicate that the RSA trapdoor permutation is not anonymous and neither are the standard encryption schemes based on it. We provide a variant of RSA-OAEP that provides anonymity in the random oracle model assuming RSA is one-way. We also give constructions of anonymous trapdoor permutations, assuming RSA is one-way, which yield anonymous encryption schemes in the standard model.

Abstract. We investigate the all-or-nothing encryption paradigm which was introduced by Rivest as a new mode of operation for block ciphers. The paradigm involves composing an all-or-nothing transform (AONT) with an ordinary encryption mode. The goal is to have secure encryption modes with the additional property that exhaustive key-search attacks on them are slowed down by a factor equal to the number of blocks in the ciphertext. We give a new notion concerned with the privacy of keys that provably captures this key-search resistance property. We suggest a new characterization of AONTs and establish that the resulting all-or-nothing encryption paradigm yields secure encryption modes that also meet this notion of key privacy. A consequence of our new characterization is that we get more efficient ways of instantiating the all-or-nothing encryption paradigm. We describe a simple block-cipher-based AONT and prove it secure in the Shannon Model of a block cipher. We also give attacks against alternate paradigms that were believed to have the above keysearch resistance property.

Abstract. We study Pseudorandom Number Generators (PRNGs) as used in practice. We first give a general security framework for PRNGs, incorporating the attacks that users are typically concerned about. We then analyze the most popular ones, including the ANSI X9.17 PRNG and the FIPS 186 PRNG. Our results also suggest ways in which these PRNGs can be made more efficient and more secure.