10 research outputs found
Randomness Condensers for Efficiently Samplable, Seed-Dependent Sources
We initiate a study of randomness condensers for sources that are efficiently samplable but may depend on the seed of the con- denser. That is, we seek functions Cond : {0, 1}n ×{0, 1}d → {0, 1}m such that if we choose a random seed S ← {0,1}d, and a source X = A(S) is generated by a randomized circuit A of size t such that X has min- entropy at least k given S, then Cond(X;S) should have min-entropy at least some k′ given S. The distinction from the standard notion of ran- domness condensers is that the source X may be correlated with the seed S (but is restricted to be efficiently samplable). Randomness extractors of this type (corresponding to the special case where k′ = m) have been implicitly studied in the past (by Trevisan and Vadhan, FOCS ‘00). We show that:
– Unlike extractors, we can have randomness condensers for samplable, seed-dependent sources whose computational complexity is smaller than the size t of the adversarial sampling algorithm A. Indeed, we show that sufficiently strong collision-resistant hash functions are seed-dependent condensers that produce outputs with min-entropy k′ = m − O(log t), i.e. logarithmic entropy deficiency.
– Randomness condensers suffice for key derivation in many crypto- graphic applications: when an adversary has negligible success proba- bility (or negligible “squared advantage” [3]) for a uniformly random key, we can use instead a key generated by a condenser whose output has logarithmic entropy deficiency.
– Randomness condensers for seed-dependent samplable sources that are robust to side information generated by the sampling algorithm imply soundness of the Fiat-Shamir Heuristic when applied to any constant-round, public-coin interactive proof system.Engineering and Applied Science
On Foundations of Protecting Computations
Information technology systems have become indispensable to uphold our
way of living, our economy and our safety. Failure of these systems can have
devastating effects. Consequently, securing these systems against malicious
intentions deserves our utmost attention.
Cryptography provides the necessary foundations for that purpose. In
particular, it provides a set of building blocks which allow to secure larger
information systems. Furthermore, cryptography develops concepts and tech-
niques towards realizing these building blocks. The protection of computations
is one invaluable concept for cryptography which paves the way towards
realizing a multitude of cryptographic tools. In this thesis, we contribute to
this concept of protecting computations in several ways.
Protecting computations of probabilistic programs. An indis-
tinguishability obfuscator (IO) compiles (deterministic) code such that it
becomes provably unintelligible. This can be viewed as the ultimate way
to protect (deterministic) computations. Due to very recent research, such
obfuscators enjoy plausible candidate constructions.
In certain settings, however, it is necessary to protect probabilistic com-
putations. The only known construction of an obfuscator for probabilistic
programs is due to Canetti, Lin, Tessaro, and Vaikuntanathan, TCC, 2015 and
requires an indistinguishability obfuscator which satisfies extreme security
guarantees. We improve this construction and thereby reduce the require-
ments on the security of the underlying indistinguishability obfuscator.
(Agrikola, Couteau, and Hofheinz, PKC, 2020)
Protecting computations in cryptographic groups. To facilitate
the analysis of building blocks which are based on cryptographic groups,
these groups are often overidealized such that computations in the group
are protected from the outside. Using such overidealizations allows to prove
building blocks secure which are sometimes beyond the reach of standard
model techniques. However, these overidealizations are subject to certain
impossibility results. Recently, Fuchsbauer, Kiltz, and Loss, CRYPTO, 2018
introduced the algebraic group model (AGM) as a relaxation which is closer
to the standard model but in several aspects preserves the power of said
overidealizations. However, their model still suffers from implausibilities.
We develop a framework which allows to transport several security proofs
from the AGM into the standard model, thereby evading the above implausi-
bility results, and instantiate this framework using an indistinguishability
obfuscator.
(Agrikola, Hofheinz, and Kastner, EUROCRYPT, 2020)
Protecting computations using compression. Perfect compression
algorithms admit the property that the compressed distribution is truly
random leaving no room for any further compression. This property is
invaluable for several cryptographic applications such as “honey encryption”
or password-authenticated key exchange. However, perfect compression
algorithms only exist for a very small number of distributions. We relax the
notion of compression and rigorously study the resulting notion which we
call “pseudorandom encodings”. As a result, we identify various surprising
connections between seemingly unrelated areas of cryptography. Particularly,
we derive novel results for adaptively secure multi-party computation which
allows for protecting computations in distributed settings. Furthermore, we
instantiate the weakest version of pseudorandom encodings which suffices
for adaptively secure multi-party computation using an indistinguishability
obfuscator.
(Agrikola, Couteau, Ishai, Jarecki, and Sahai, TCC, 2020
International Symposium on Mathematics, Quantum Theory, and Cryptography
This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography
International Symposium on Mathematics, Quantum Theory, and Cryptography
This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Diseños de protocolos criptográficos: nuevas propuestas basadas en grafos
Se destaca el papel que la teoría de grafos puede jugar en el entorno de la criptografía moderna. Se introduce también una nueva metodología de diseño en el campo de los protocolos criptográficos. Entre los protocolos estudiados destacan as de transferencia inconsciente y compromiso de bits por se considerados primitivos esenciales para el diseño de esquemas criptográficos más complejos. También se presta especial atención a las demostraciones de conocimiento nulo aportando nuevos algoritmos orientados a resolver el problema de la identificación
A Salad of Block Ciphers
This book is a survey on the state of the art in block cipher design and analysis.
It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months.
However, it is also in a self-contained, useable, and relatively polished state, and for this reason
I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much.
At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people