| This work examines two aspects of cryptography, the evaluation of the security of an existing encryption algorithm and the distributed creation of digital signatures for a group or organization.; The first part of the thesis describes a new type of cryptanalytic attack, differential-linear cryptanalysis, and evaluates its effectiveness against the data encryption standard (DES). Differential-linear cryptanalysis is very efficient against a reduced 8-round variant of DES, recovering 10 bits of key with 80% probability of success using only 512 chosen plaintexts. The probability of success increases to 95% using 768 chosen plaintexts. While comparable in speed to existing attacks, this attack represents an order of magnitude improvement in the amount of required text. In addition to describing the basic attack, we examine the effects of using multiple parity relations, list decoding, and recovering additional bits of key. The attack is also extended to 10 and 12-round DES.; The second part of the thesis presents a 2-out-of-l threshold signature scheme based on the digital signature standard. A t-out-of-l threshold signature scheme allows l members of a group to share a private key such that any t of them can create a signature, while fewer than t cannot. Most of these schemes require a single trusted party to create the secret key and calculate the l shares. Our scheme does not require such a trusted party, making it an attractive alternative for situations in which there is no single trusted authority. Two possible generalizations of this scheme are introduced. Both generalizations allow more than two signers and have a provable level of security. Although the two generalizations are of less practical interest, it is hoped that they might lead to a more acceptable general solution for DSS threshold signatures. |
