Agricultural soils are subjected to many applied mechanical stresses that influence their behavior. Stresses arise from tillage machines, seeders and chemicals applicators, tractors, and equipment for harvest and transport. Applied stresses may compact or loosen the bulk soil. Micro sections of soil (aggregates or clods) may be compacted during tillage while the bulk soil is loosened. Because most granular soils are combined into structural units of varying sizes with different strengths and properties, prediction of the effect of stresses on the behavior of bulk soils is difficult. The basic strength properties of soil are determined by many fac tors: the size distribution of particles, chemical and mineralogical properties of inorganic clay fraction, the organic matter content and composition, the water content and the stress history. These factors combine and interact to produce many possible behavior patterns. Changes in structure of the soil from applied stresses and biologi cal reactions may profoundly influence storage and transmission of water, heat, and air, and the mechanical resistance to penetration by plant roots. They may also affect the traction of vehicles. Manipulation of structural properties of soils by tillage implements is a major cost under most crop production systems. Reduced energy use is also a significant conservation objective. Improved management systems are very dependent upon a better understanding of soils' response to applied stresses. The content of this book resulted from a NATO Advanced Research Workshop held in St. Paul, Minnesota, U.S.A. September 13-16, 1988."

Agricultural soils are subjected to many applied mechanical stresses that influence their behavior. Stresses arise from tillage machines, seeders and chemicals applicators, tractors, and equipment for harvest and transport. Applied stresses may compact or loosen the bulk soil. Micro sections of soil (aggregates or clods) may be compacted during tillage while the bulk soil is loosened. Because most granular soils are combined into structural units of varying sizes with different strengths and properties, prediction of the effect of stresses on the behavior of bulk soils is difficult. The basic strength properties of soil are determined by many fac tors: the size distribution of particles, chemical and mineralogical properties of inorganic clay fraction, the organic matter content and composition, the water content and the stress history. These factors combine and interact to produce many possible behavior patterns. Changes in structure of the soil from applied stresses and biologi cal reactions may profoundly influence storage and transmission of water, heat, and air, and the mechanical resistance to penetration by plant roots. They may also affect the traction of vehicles. Manipulation of structural properties of soils by tillage implements is a major cost under most crop production systems. Reduced energy use is also a significant conservation objective. Improved management systems are very dependent upon a better understanding of soils' response to applied stresses. The content of this book resulted from a NATO Advanced Research Workshop held in St. Paul, Minnesota, U.S.A. September 13-16, 1988."

Recently, there has been a lot of interest in provably "good" pseudo-random number generators [lo, 4, 14, 31. These cryptographically secure generators are "good" in the sense that they pass all probabilistic polynomial time statistical tests. However, despite these nice properties, the secure generators known so far suffer from the han- cap of being inefiicient; the most efiicient of these take n2 steps (one modular multip- cation, n being the length of the seed) to generate one bit. Pseudc-random number g- erators that are currently used in practice output n bits per multiplication (n2 steps). An important open problem was to output even two bits on each multiplication in a cryptographically secure way. This problem was stated by Blum, Blum & Shub [3] in the context of their z2 mod N generator. They further ask: how many bits can be o- put per multiplication, maintaining cryptographic security? In this paper we state a simple condition, the XOR-Condition and show that any generator satisfying this condition can output logn bits on each multiplication. We show that the XOR-Condition is satisfied by the lop least significant bits of the z2-mod N generator. The security of the z2 mod N generator was based on Quadratic Residu- ity [3]. This generator is an example of a Trapdoor Generator [13], and its trapdoor properties have been used in protocol design. We strengthen the security of this gene- tor by proving it as hard as factoring.

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