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Unbalanced Oil and Vinegar Signature Schemes
 IN ADVANCES IN CRYPTOLOGY — EUROCRYPT 1999
, 1999
"... In [15], J. Patarin designed a new scheme, called "Oil and Vinegar", for computing asymmetric signatures. It is very simple, can be computed very fast (both in secret and public key) and requires very little RAM in smartcard implementations. The idea consists in hiding quadratic equations ..."
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Cited by 47 (3 self)
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In [15], J. Patarin designed a new scheme, called "Oil and Vinegar", for computing asymmetric signatures. It is very simple, can be computed very fast (both in secret and public key) and requires very little RAM in smartcard implementations. The idea consists in hiding quadratic equations in n unknowns called "oil" and v = n unknowns called "vinegar" over a finite field K, with linear secret functions. This original scheme was broken in [9] by A. Kipnis and A. Shamir. In this paper, we study some very simple variations of the original scheme where v ? n (instead of v = n). These schemes are called "Unbalanced Oil and Vinegar" (UOV), since we have more "vinegar" unknowns than "oil" unknowns. We show that, when v ' n, the attack of [9] can be extended, but when v 2n for example, the security of the scheme is still an open problem. Moreover, when v ' n 2 2 , the security of the scheme is exactly equivalent (if we accept a very natural but not proved property) to the problem of solvi...
A Customisable Memory Management Framework
, 1994
"... Memory management is a critical issue for many large objectoriented applications, but in C++ only explicit memory reclamation through the delete operator is generally available. We analyse different possibilities for memory management in C++ and present a dynamic memory management framework which c ..."
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Cited by 24 (2 self)
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Memory management is a critical issue for many large objectoriented applications, but in C++ only explicit memory reclamation through the delete operator is generally available. We analyse different possibilities for memory management in C++ and present a dynamic memory management framework which can be customised to the need of specific applications. The framework allows full integration and coexistence of different memory management techniques. The Customisable Memory Management (CMM) is based on a primary collector which exploits an evolution of Bartlett's mostly copying garbage collector. Specialised collectors can be built for separate memory heaps. A Heap class encapsulates the allocation strategy for each heap. We show how to emulate different garbage collection styles or userspecific memory management techniques. The CMM is implemented in C++ without any special support in the language or the compiler. The techniques used in the CMM are general enough to be applicable also to...
The special Schubert calculus is real
 Electronic Research Announcements of the AMS 5:35–39
, 1999
"... Abstract. We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real. ERA of the AMS 5 (1999), pp. 35–39. Fulton asked how many solut ..."
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Cited by 19 (9 self)
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Abstract. We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real. ERA of the AMS 5 (1999), pp. 35–39. Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with respect to some general fixed figures [5]. For the problem of plane conics tangent to five general conics, the (surprising) answer is that all 3264 may be real [10]. Recently, Dietmaier has shown that all 40 positions of the Stewart platform in robotics may be real [2]. Similarly, given any problem of enumerating lines in projective space incident on some general fixed linear subspaces, there are real fixed subspaces such that each of the (finitely many) incident lines are real [13]. Other examples are shown in [12, 14], and the case of 462 4planes meeting 12 general 3planes in R 7 is due to an heroic symbolic computation [4]. For any problem of enumerating pplanes having excess intersection with a collection
Some real and unreal enumerative geometry for Flag manifolds
 S4] [SVV] [St] [V1] [V2] [V3] F. Sottile, personal communication
"... Abstract. We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems on flag manifolds may have all their so ..."
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Cited by 10 (4 self)
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Abstract. We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems on flag manifolds may have all their solutions be real and modify this method to show that another class may have no real solutions, which is a new phenomenon. This method originated in a numerical homotopy continuation algorithm adapted to the special Schubert calculus on Grassmannians and in principle gives optimal numerical homotopy algorithms for finding explicit solutions to these other enumerative problems.
Customising Object Allocation
 In ECOOP '94  ObjectOriented Programming
, 1994
"... . Automatic garbage collection relieves programmers from the burden of managing memory themselves and several techniques have been developed that make garbage collection feasible in many situations, including real time applications or within traditional programming languages. However optimal perform ..."
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Cited by 7 (2 self)
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. Automatic garbage collection relieves programmers from the burden of managing memory themselves and several techniques have been developed that make garbage collection feasible in many situations, including real time applications or within traditional programming languages. However optimal performance cannot always be achieved by a uniform general purpose solution. Sometimes an algorithm exhibits a predictable pattern of memory usage that could be better handled specifically, delaying as much as possible the intervention of the general purpose collector. This leads to the requirement for algorithm specific customisation of the collector strategies. We present a dynamic memory management framework which can be customised to the needs of an algorithm, while preserving the convenience of automatic collection in the normal case. The Customisable Memory Management (CMM) organizes memory in multiple heaps. Each heap is defined as a C++ class which encapsulates a particular storage discipli...
Experimentation at the Frontiers of Reality in Schubert Calculus
, 2009
"... Abstract. We describe the setup, design, and execution of a computational experiment utilizing a supercomputer that is helping to formulate and test conjectures in the real Schubert calculus. Largely using machines in instructional computer labs during offhours and University breaks, it consumed in ..."
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Cited by 2 (2 self)
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Abstract. We describe the setup, design, and execution of a computational experiment utilizing a supercomputer that is helping to formulate and test conjectures in the real Schubert calculus. Largely using machines in instructional computer labs during offhours and University breaks, it consumed in excess of 350 GigaHertzyears of computing in its first six months of operation, solving over 1.1 billion polynomial systems. This experiment can serve as a model for other large scale mathematical investigations.