Control and Cybernetics Contemporary Cryptology

The book here reviewed consists of several articles written by different authors. We provide below short characteristics of each of the articles in the book. 1. Efficient distributed computation modulo a shared secret (Dario Catalano) The article concerns the subject of distributed computation. This is realized by the secret sharing protocols. The author presents several kinds of such protocols: additive sharing over Z or Z q , and polynomial sharing over Z or Z q. The mutual conversions among different secret sharing methods are presented. Then, the author considers the distributed modular reduction applying the Newton iteration method. These methods allow for approximating 1/p, where p is a prime number, in a distributive manner. Moreover, the conventional arithmeti-cal operations, such as adding and multiplication, are performed in a distributive manner. By combining the above ideas, the modular powering, inversion and computation a(mod p) is made through distributive computation. The joint generation of random values and the modular distributive arithmetic constitute, therefore, a sufficient background for applying the Miller-Rabin probabilistic primality tests, in order to generate the prime numbers in a distributive manner. This is the way, in which cryptographic systems might be generated in a distributive model. Consider, for example, the RSA cryptosystem. If two random primes are generated, we are able to compute their product. Then the encryption and decryption exponents are generated-the first one as a random shared secret and the other as the inverse in the modular arithmetic. In this manner the RSA system could be realized in a distributed way. In the similar manner other public key cryptosystems could be incorporated in distributive computational model. The distributive model for the RSA cryptosystem was realized for the first time by Boneh and Franklin in 1997. Catalano's article represents a good and elementary introduction in this area. Moreover, what is also important, the efficiency, communication costs and computational bounds for the presented protocols are considered.