Parallel cryptanalysis

R.F. Niederhagen

Research output: ThesisPhd Thesis 1 (Research TU/e / Graduation TU/e)Academic

Abstract

Most of today’s cryptographic primitives are based on computations that are hard to perform for a potential attacker but easy to perform for somebody who is in possession of some secret information, the key, that opens a back door in these hard computations and allows them to be solved in a small amount of time. To estimate the strength of a cryptographic primitive it is important to know how hard it is to perform the computation without knowledge of the secret back door and to get an understanding of how much money or time the attacker has to spend. Usually a cryptographic primitive allows the cryptographer to choose parameters that make an attack harder at the cost of making the computations using the secret key harder as well. Therefore designing a cryptographic primitive imposes the dilemma of choosing the parameters strong enough to resist an attack up to a certain cost while choosing them small enough to allow usage of the primitive in the real world, e.g. on small computing devices like smart phones. This thesis investigates three different attacks on particular cryptographic systems: Wagner’s generalized birthday attack is applied to the compression function of the hash function FSB. Pollard’s rho algorithm is used for attacking Certicom’s ECC Challenge ECC2K-130. The implementation of the XL algorithm has not been specialized for an attack on a specific cryptographic primitive but can be used for attacking some cryptographic primitives by solving multivariate quadratic systems. All three attacks are general attacks, i.e. they apply to various cryptographic systems; the implementations of Wagner’s generalized birthday attack and Pollard’s rho algorithm can be adapted for attacking other primitives than those given in this thesis. The three attacks have been implemented on different parallel architectures. XL has been parallelized using the Block Wiedemann algorithm on a NUMA system using OpenMP and on an Infiniband cluster using MPI. Wagner’s attack was performed on a distributed system of 8 multi-core nodes connected by an Ethernet network. The work on Pollard’s Rho algorithm is part of a large research collaboration with several research groups; the computations are embarrassingly parallel and are executed in a distributed fashion in several facilities with almost negligible communication cost. This dissertation presents implementations of the iteration function of Pollard’s Rho algorithm on Graphics Processing Units and on the Cell Broadband Engine.
LanguageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • TUE : Department of Mathematics and Computer Science
Supervisors/Advisors
  • Lange, Tanja, Promotor
  • Bernstein, Daniel, Promotor
  • Cheng, C.M., Copromotor, External person
Award date23 Apr 2012
Place of PublicationEindhoven
Publisher
Print ISBNs978-90-386-3128-8
DOIs
StatePublished - 2012

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Hash functions
Parallel architectures
Ethernet
Costs
Engines
Communication
Graphics processing unit

Cite this

Niederhagen, R. F. (2012). Parallel cryptanalysis Eindhoven: Technische Universiteit Eindhoven DOI: 10.6100/IR731259
Niederhagen, R.F.. / Parallel cryptanalysis. Eindhoven : Technische Universiteit Eindhoven, 2012. 110 p.
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title = "Parallel cryptanalysis",
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Niederhagen, RF 2012, 'Parallel cryptanalysis', Doctor of Philosophy, TUE : Department of Mathematics and Computer Science, Eindhoven. DOI: 10.6100/IR731259

Parallel cryptanalysis. / Niederhagen, R.F.

Eindhoven : Technische Universiteit Eindhoven, 2012. 110 p.

Research output: ThesisPhd Thesis 1 (Research TU/e / Graduation TU/e)Academic

TY - THES

T1 - Parallel cryptanalysis

AU - Niederhagen,R.F.

PY - 2012

Y1 - 2012

N2 - Most of today’s cryptographic primitives are based on computations that are hard to perform for a potential attacker but easy to perform for somebody who is in possession of some secret information, the key, that opens a back door in these hard computations and allows them to be solved in a small amount of time. To estimate the strength of a cryptographic primitive it is important to know how hard it is to perform the computation without knowledge of the secret back door and to get an understanding of how much money or time the attacker has to spend. Usually a cryptographic primitive allows the cryptographer to choose parameters that make an attack harder at the cost of making the computations using the secret key harder as well. Therefore designing a cryptographic primitive imposes the dilemma of choosing the parameters strong enough to resist an attack up to a certain cost while choosing them small enough to allow usage of the primitive in the real world, e.g. on small computing devices like smart phones. This thesis investigates three different attacks on particular cryptographic systems: Wagner’s generalized birthday attack is applied to the compression function of the hash function FSB. Pollard’s rho algorithm is used for attacking Certicom’s ECC Challenge ECC2K-130. The implementation of the XL algorithm has not been specialized for an attack on a specific cryptographic primitive but can be used for attacking some cryptographic primitives by solving multivariate quadratic systems. All three attacks are general attacks, i.e. they apply to various cryptographic systems; the implementations of Wagner’s generalized birthday attack and Pollard’s rho algorithm can be adapted for attacking other primitives than those given in this thesis. The three attacks have been implemented on different parallel architectures. XL has been parallelized using the Block Wiedemann algorithm on a NUMA system using OpenMP and on an Infiniband cluster using MPI. Wagner’s attack was performed on a distributed system of 8 multi-core nodes connected by an Ethernet network. The work on Pollard’s Rho algorithm is part of a large research collaboration with several research groups; the computations are embarrassingly parallel and are executed in a distributed fashion in several facilities with almost negligible communication cost. This dissertation presents implementations of the iteration function of Pollard’s Rho algorithm on Graphics Processing Units and on the Cell Broadband Engine.

AB - Most of today’s cryptographic primitives are based on computations that are hard to perform for a potential attacker but easy to perform for somebody who is in possession of some secret information, the key, that opens a back door in these hard computations and allows them to be solved in a small amount of time. To estimate the strength of a cryptographic primitive it is important to know how hard it is to perform the computation without knowledge of the secret back door and to get an understanding of how much money or time the attacker has to spend. Usually a cryptographic primitive allows the cryptographer to choose parameters that make an attack harder at the cost of making the computations using the secret key harder as well. Therefore designing a cryptographic primitive imposes the dilemma of choosing the parameters strong enough to resist an attack up to a certain cost while choosing them small enough to allow usage of the primitive in the real world, e.g. on small computing devices like smart phones. This thesis investigates three different attacks on particular cryptographic systems: Wagner’s generalized birthday attack is applied to the compression function of the hash function FSB. Pollard’s rho algorithm is used for attacking Certicom’s ECC Challenge ECC2K-130. The implementation of the XL algorithm has not been specialized for an attack on a specific cryptographic primitive but can be used for attacking some cryptographic primitives by solving multivariate quadratic systems. All three attacks are general attacks, i.e. they apply to various cryptographic systems; the implementations of Wagner’s generalized birthday attack and Pollard’s rho algorithm can be adapted for attacking other primitives than those given in this thesis. The three attacks have been implemented on different parallel architectures. XL has been parallelized using the Block Wiedemann algorithm on a NUMA system using OpenMP and on an Infiniband cluster using MPI. Wagner’s attack was performed on a distributed system of 8 multi-core nodes connected by an Ethernet network. The work on Pollard’s Rho algorithm is part of a large research collaboration with several research groups; the computations are embarrassingly parallel and are executed in a distributed fashion in several facilities with almost negligible communication cost. This dissertation presents implementations of the iteration function of Pollard’s Rho algorithm on Graphics Processing Units and on the Cell Broadband Engine.

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M3 - Phd Thesis 1 (Research TU/e / Graduation TU/e)

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Niederhagen RF. Parallel cryptanalysis. Eindhoven: Technische Universiteit Eindhoven, 2012. 110 p. Available from, DOI: 10.6100/IR731259