1,565 research outputs found
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Semantic Security and Indistinguishability in the Quantum World
At CRYPTO 2013, Boneh and Zhandry initiated the study of quantum-secure
encryption. They proposed first indistinguishability definitions for the
quantum world where the actual indistinguishability only holds for classical
messages, and they provide arguments why it might be hard to achieve a stronger
notion. In this work, we show that stronger notions are achievable, where the
indistinguishability holds for quantum superpositions of messages. We
investigate exhaustively the possibilities and subtle differences in defining
such a quantum indistinguishability notion for symmetric-key encryption
schemes. We justify our stronger definition by showing its equivalence to novel
quantum semantic-security notions that we introduce. Furthermore, we show that
our new security definitions cannot be achieved by a large class of ciphers --
those which are quasi-preserving the message length. On the other hand, we
provide a secure construction based on quantum-resistant pseudorandom
permutations; this construction can be used as a generic transformation for
turning a large class of encryption schemes into quantum indistinguishable and
hence quantum semantically secure ones. Moreover, our construction is the first
completely classical encryption scheme shown to be secure against an even
stronger notion of indistinguishability, which was previously known to be
achievable only by using quantum messages and arbitrary quantum encryption
circuits.Comment: 37 pages, 2 figure
Stream cipher based on quasigroup string transformations in
In this paper we design a stream cipher that uses the algebraic structure of
the multiplicative group \bbbz_p^* (where p is a big prime number used in
ElGamal algorithm), by defining a quasigroup of order and by doing
quasigroup string transformations. The cryptographical strength of the proposed
stream cipher is based on the fact that breaking it would be at least as hard
as solving systems of multivariate polynomial equations modulo big prime number
which is NP-hard problem and there are no known fast randomized or
deterministic algorithms for solving it. Unlikely the speed of known ciphers
that work in \bbbz_p^* for big prime numbers , the speed of this stream
cipher both in encryption and decryption phase is comparable with the fastest
symmetric-key stream ciphers.Comment: Small revisions and added reference
Partial-indistinguishability obfuscation using braids
An obfuscator is an algorithm that translates circuits into
functionally-equivalent similarly-sized circuits that are hard to understand.
Efficient obfuscators would have many applications in cryptography. Until
recently, theoretical progress has mainly been limited to no-go results. Recent
works have proposed the first efficient obfuscation algorithms for classical
logic circuits, based on a notion of indistinguishability against
polynomial-time adversaries. In this work, we propose a new notion of
obfuscation, which we call partial-indistinguishability. This notion is based
on computationally universal groups with efficiently computable normal forms,
and appears to be incomparable with existing definitions. We describe universal
gate sets for both classical and quantum computation, in which our definition
of obfuscation can be met by polynomial-time algorithms. We also discuss some
potential applications to testing quantum computers. We stress that the
cryptographic security of these obfuscators, especially when composed with
translation from other gate sets, remains an open question.Comment: 21 pages,Proceedings of TQC 201
Homomorphic encryption and some black box attacks
This paper is a compressed summary of some principal definitions and concepts
in the approach to the black box algebra being developed by the authors. We
suggest that black box algebra could be useful in cryptanalysis of homomorphic
encryption schemes, and that homomorphic encryption is an area of research
where cryptography and black box algebra may benefit from exchange of ideas
A Novel Latin Square Image Cipher
In this paper, we introduce a symmetric-key Latin square image cipher (LSIC)
for grayscale and color images. Our contributions to the image encryption
community include 1) we develop new Latin square image encryption primitives
including Latin Square Whitening, Latin Square S-box and Latin Square P-box ;
2) we provide a new way of integrating probabilistic encryption in image
encryption by embedding random noise in the least significant image bit-plane;
and 3) we construct LSIC with these Latin square image encryption primitives
all on one keyed Latin square in a new loom-like substitution-permutation
network. Consequently, the proposed LSIC achieve many desired properties of a
secure cipher including a large key space, high key sensitivities, uniformly
distributed ciphertext, excellent confusion and diffusion properties,
semantically secure, and robustness against channel noise. Theoretical analysis
show that the LSIC has good resistance to many attack models including
brute-force attacks, ciphertext-only attacks, known-plaintext attacks and
chosen-plaintext attacks. Experimental analysis under extensive simulation
results using the complete USC-SIPI Miscellaneous image dataset demonstrate
that LSIC outperforms or reach state of the art suggested by many peer
algorithms. All these analysis and results demonstrate that the LSIC is very
suitable for digital image encryption. Finally, we open source the LSIC MATLAB
code under webpage https://sites.google.com/site/tuftsyuewu/source-code.Comment: 26 pages, 17 figures, and 7 table
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