Abstract. The exponentiation function in a finite field of order p (a prime number) is believed to be a one-way function. It is well known that O(log tog p) bits are simultaneously hazd for this function. We consider a special case of this problem, the discrete logarithm with short exponents, which is also believed to be hard to compute. Under this intractibility assumption we show that discrete exponentiation modulo a prime p can hide n-w(log n) bits (n = ~log p] and p = 2q § where q is also a prime). We prove simultaneous security by showing that any information about the n -w(log n) bits can be used to discover the discrete log of g' rood p where s has w(log n) bits. For all practical purposes, the size of s can be a constant c bits. This leads to a very efficient pseudo-random number generator which produces n -c bits per iteration. For example, when n = 1024 bits and c = 128 bits our pseudo-random number generator produces a tittle less than 900 bits per exponentiation.

Packet data is expected to dominate third generation wireless networks, unlike current generation voice networks. This opens up new and interesting problems. Physical and link layer issues have been studied extensively, while resource allocation and scheduling issues have not been addressed satisfactorily.In this work, we address resource management on the downlink of CDMA packet data networks. Network performance (for example, capacity) has been addressed, but user centric performance has not received much attention. Recently, various non-traditional scheduling schemes based on new metrics have been proposed, and target user performance (mostly without reference to wireless). We adapt these metrics to the CDMA context, and establish some new results for the ofitine scheduling problem. In addition, we modify a large class of online algorithms to work in our setup and conduct a wide range of experiments. Based on detailed simulations, we infer that:• Algorithms which exploit "request sizes" seem to outperform those that do not. Among these, algorithms that also exploit channel conditions provide significantly higher network throughput.• Depending on continuous or discretized bandwidth conditions, either pure time multiplexing or a combination of time and code multiplexing strikes an excellent balance between user satisfaction and network performance.• Discrete bandwidth conditions can lead to degraded user level performance without much impact on network performance. We argue that the discretization needs to be fine tuned to address this shortcoming.

Abstract. We provide new constructions for Luby-Rackoae block ciphers which are eaecient in terms of computations and key material used. Next, we show that we can make some security guarantees for Luby-Rackoae block ciphers under much w eaker and more practical assumptions about the underlying function; namely, that the underlying function is a secure Message Authentication Code. Finally, w e provide a SHA-1 based example block cipher called Sha-zam.

Abstract. Existing block ciphers operate on a fixed-input-length (FIL) block size (e.g., 64-bits for DES). Often, one needs a variable-inputlength (VIL) primitive that can operate on a different size input; it is, however, undesirable to construct this primitive from "scratch." This paper contains two constructions that start with a fixed-input-length block cipher and show how to securely convert it to a variable-input-length block cipher without making any additional cryptographic assumptions. Both constructions model the FIL block cipher as a pseudorandom permutation (PRP) -that is, indistinguishable from a random permutation against adaptive chosen plaintext attack. The first construction converts it to a VIL PRP and is an efficiency improvement over the scheme of Bellare and Rogaway [4]. The second construction converts it to a VIL super pseudorandom permutation (SPRP) -that is, the resulting VIL block cipher is indistinguishable from a random permutation against adaptive chosen plaintext and ciphertext attack.

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