Abstract. Textbooks tell us that a birthday attack on a hash function h with range size r requires r 1/2 trials (hash computations) to find a collision. But this is quite misleading, being true only if h is regular, meaning all points in the range have the same number of pre-images under h; if h is not regular, fewer trials may be required. But how much fewer? This paper addresses this question by introducing a measure of the “amount of regularity ” of a hash function that we call its balance, and then providing estimates of the success-rate of the birthday attack, and the expected number of trials to find a collision, as a function of the balance of the hash function being attacked. In particular, we will see that the number of trials can be significantly less than r 1/2 for hash functions of low balance. This leads us to examine popular design principles, such as the MD (Merkle-Damg˚ard) transform, from the point of view of balance preservation, and to mount experiments to determine the balance of popular hash functions. 1

We develop a public key cryptosystem whose security is based on the intractability of the ideal membership problem for a noncommutative algebra over a finite field. We show that this system, which is the noncommutative analogue of the Polly Cracker cryptosystem, is more secure than the commutative version. This is due to the fact that there are a number of ideals of noncommutative algebras (over finite fields) that have infinite reduced Gröbner bases, and can be used to generate a public key. We present classes of such ideals and prove that they do not have a finite Gröbner basis under any admissible order. We also examine various techniques to realize finite Gröbner bases, in order to determine whether these ideals can be used effectively in the design of a public key cryptosystem. We then show how some of these classes of ideals, which have infinite reduced Gröbner bases, can be used to design a public key cryptosystem. We also study various techniques of encryption. Finally, we study techniques of cryptanalysis that may be used to attack the cryptosystems that we present. We show how poorly constructed public keys can in fact, reveal the private key, and discuss techniques to design public keys that adequately

The aims of this research are to give a precise description of a new homomorphic public-key encryption scheme proposed by Grigoriev and Ponomarenko [7] in 2004 and to break Grigoriev and Ponomarenko homomorphic public-key cryptosystem. Firstly, we prove some properties of linear fractional transformations. We analyze the Xn-representation algorithm which is used in the decryption scheme of Grigoriev and Ponomarenko homomorphic public-key cryptosystem and by these properties of the linear fractional transformations, we correct and modify the Xn-representation algorithm. We implement the modified Xn-representation algorithm by program-ming it and we prove the correctness of the modified Xn-representation algorithm. Secondly, we find an explicit formula to compute the X(n, S)-representations of ele-ments of the group Γn. The X(n, S)-representation algorithm is used in the decryp-tion scheme of Grigoriev and Ponomarenko homomorphic public-key cryptosystem and we modify the X(n, S)-representation algorithm. We implement the modified X(n, S)-representation algorithm by programming it and we justify the modified

Alice and Bob share a correlated composite quantum system AB. If AB is used as the key for a one-time pad cryptographic system, we show that the maximum amount of information that Alice can send securely to Bob is the quantum mutual information of AB. 1 The one-time pad and mutual information A one-time pad [1] is a cryptographic protocol in which communicators Alice and Bob initially have correlated random variables, collectively called the “key”, that are not correlated with any variables possessed by a potential eavesdropper Eve. (In most discussions, the key variables possessed by Alice and Bob are supposed to be perfectly correlated—e.g., they are identical copies of the same secret string of bits. We consider the more general case.) If the key variables are used only once, they allow Alice to send Bob a perfectly secret message over a public communication channel. The value of a key as a resource is the amount of information that can be sent secretly by

A novel strategy to encrypt covert information (code) via unitary projections into the null spaces of ill-conditioned eigenstructures of multiple host statistical distributions, inferred from incomplete constraints, is presented. The host pdf ’s are inferred using the maximum entropy principle. The projection of the covert information is dependent upon the pdf ’s of the host statistical distributions. The security of the encryption/decryption strategy is based on the extreme instability of the encoding process. A self-consistent procedure to derive keys for both symmetric and asymmetric cryptography is presented. The advantages of using a multiple pdf model to achieve encryption of covert information are briefly highlighted. Numerical simulations exemplify the efficacy of the model.

Abstract not found

To Ami, Abba and Ammar for their endless love and supportiii

As the both the requirement and demand for secure systems increases, so to will the ubiquitousness of cryptography. The most secure cryptographic schemes often involve complicated algorithms and are by no means cheap to implement on standard hardware, and it is this that has led to the development of cryptographic hardware accelerators. Optimizing software to take advantage of these hardware devices is a problem akin to that of effective parallelization and this project aims to determine how these accelerators perform and under what conditions their use is cost-effective. Through the development of code designed to exercise the particular accelerators existing on the Solaris UltraSPARC T2 via the Solaris Cryptographic Framework (SCF) the system’s performance under a variety of different conditions was assessed. A suggestion for the possible design of a benchmark exclusively for hardware accelerated cryptography is also given. The results indicate that substantial performance gains can be had with

Abstract not found

Abstract—In this paper the development of a software to encrypt messages with asymmetric cryptography is presented. In particular, is used the RSA (Rivest, Shamir and Adleman) algorithm to encrypt alphanumeric information. The software allows to generate different public keys from two prime numbers provided by the user, the user must then select a public-key to generate the corresponding private-key. To encrypt the information, the user must provide the public-key of the recipient as well as the message to be encrypted. The generated ciphertext can be sent through an insecure channel, so that would be very difficult to be interpreted by an intruder or attacker. At the end of the communication, the recipient can decrypt the original message if provide his/her public-key and his/her corresponding private-key. or a courier. Figure 1 shows a block diagram of the symmetric key cryptography [3]. The key exchange problem becomes even more difficult if many people want to exchange encrypted messages, for example on the internet. If a network communication system has n users and any two of them exchange a key, then n(n-1)/2 secret key exchanges are necessary and all those keys have to be stored securely [4].