TL;DR: In this article, the authors studied some candidate asymmetric cryptosystems based on the idea of hiding one or two rounds of small S-box computations with secret functions of degree 1 or 2.
Abstract: In this paper, we study some new “candidate” asymmetric cryptosystems based on the idea of hiding one or two rounds of small S-box computations with secret functions of degree one or two. The C” scheme of [10] (when its n i values are small can be seen as a very special case of these schemes. This C” scheme was broken in [11] due to unexpected algebraic properties. In the new schemes, those algebraic properties generally do not exist. Nevertheless, we will see that most of the “new” algorithms can also be broken and we deduce some very different cryptanalysis of C”.
TL;DR: An efficient authenticated encryption scheme with message linkage based on the discrete logarithm problem that can be combined with ElGamal encryption in a natural manner and is lower than those of the straightforward method.
TL;DR: Two encryption schemes are described which use their random oracles in a rather limited way and achieve semantic security and plaintext awareness under specified assumptions.
Abstract: A cryptographic scheme is “provably secure” if an attack on the scheme implies an attack on the underlying primitives it employs. A cryptographic scheme is “provably secure in the random-oracle model” if it uses a cryptographic hash function F and is provably secure when F is modeled by a public random function. Demonstrating that a crypto graphic scheme is provably secure in the random-oracle model engenders much assurance in the scheme's correctness. But there may remain some lingering fear that the concrete hash function which instantiates the random oracle differs from a random function in some significant way. So it is good to limit reliance on random oracles. Here we describe two encryption schemes which use their random oracles in a rather limited way. The schemes achieve semantic security and plaintext awareness under specified assumptions. One scheme uses the RSA primitive; another uses Diffie-Hellman. In either case messages longer than the modulus length can be safely and directly encrypted without relying on the hash functions modeled as random-oracles to be good for private-key encryption.