104 research outputs found
Provably Secure Integration Cryptosystem on Non-Commutative Group
Braid group is a very important non-commutative group. It is also an important tool of quantum field theory, and has good topological properties. This paper focuses on the provable security research of cryptosystem over braid group, which consists of two aspects: One, we prove that the Ko\u27s cryptosystem based on braid group is secure against chosen-plaintext-attack which proposed in CRYPTO 2000, while it dose not resist active attack. The other is to propose a new public key cryptosystem over braid group which is secure against adaptive chosen-ciphertext-attack. Our proofs are based on random oracle models, under the computational conjugacy search assumption. This kind of results have never been seen before
Post-Quantum Key Agreement Protocol based on Non-Square Integer Matrices
We present in this paper an algorithm for exchanging session keys, coupled
with a hashing encryption module. We show schemes designed for their potential
invulnerability to classical and quantum attacks. In turn, if the parameters
included were appropriate, brute-force attacks exceed the (five) security
levels used in the NIST competition of new post-quantum standards. The original
idea consists of products of rectangular matrices in Zp as public values and
whose factorization is proved to be an NP-complete problem. We present running
times as a function of the explored parameters and their link with operational
safety. To our knowledge there are no classical and quantum attacks of
polynomial complexity available at hand, remaining only the systematic
exploration of the private-key space.Comment: 12 pages, 2 tables, 29 reference
The Twin Conjugacy Search Problem and Applications
We propose a new computational problem over the noncommutative group, called the twin conjugacy search problem. This problem is related to the conjugacy search problem and can be used for almost all of the same cryptographic constructions that are based on the conjugacy search problem. However, our new problem is at least as hard as the conjugacy search problem.
Moreover, the twin conjugacy search problem has many applications. One of the most important applications, we propose a trapdoor test which can replace the function of the decision oracle. We also show other applications of the problem, including: a non-interactive key exchange protocol and a key exchange protocol, a new encryption scheme which is secure against chosen ciphertext attack, with a very simple and tight security proof and short ciphertexts, under a weak assumption, in the random oracle model
New foundations for efficient authentication, commutative cryptography, and private disjointness testing
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 105-115).This dissertation presents new constructions and security definitions related to three areas: authentication, cascadable and commutative crytpography, and private set operations. Existing works relevant to each of these areas fall into one of two categories: efficient solutions lacking formal proofs of security or provably-secure, but highly inefficient solutions. This work will bridge this gap by presenting new constructions and definitions that are both practical and provably-secure. The first contribution in the area of efficient authentication is a provably-secure authentication protocol named HB+. The HB+ protocol is efficient enough to be implemented on extremely low-cost devices, or even by a patient human with a coin to flip. The security of HB+ is based on the hardness of a long-standing learning problem that is closely related to coding theory. HB+ is the first authentication protocol that is both practical for low-cost devices, like radio frequency identification (RFID) tags, and provably secure against active adversaries. The second contribution of this work is a new framework for defining and proving the security of cascadable cryptosystems, specifically commutative cryptosystems.(cont.) This new framework addresses a gap in existing security definitions that fail to handle cryptosystems where ciphertexts produced by cascadable encryption and decryption perations may contain some message-independent history. Several cryptosystems, including a new, practical commutative cryptosystem, are proven secure under this new framework. Finally, a new and efficient private disjointness testing construction named HW is offered. Unlike previous constructions, HW is secure in the face of malicious parties, but without the need for random oracles or expensive zero-knowledge protocols. HW is as efficient as previous constructions and may be implemented using standard software libraries. The security of HW is based on a novel use of subgroup assumptions. These assumptions may prove useful in solving many other private set operation problems.by Stephen A. Weis.Ph.D
A Novel Provably Secure Key Agreement Protocol Based On Binary Matrices
In this paper, a new key agreement protocol is presented. The protocol uses
exponentiation of matrices over GF(2) to establish the key agreement. Security
analysis of the protocol shows that the shared secret key is indistinguishable
from the random under Decisional Diffie-Hellman (DDH) assumption for subgroup
of matrices over GF(2) with prime order, and furthermore, the analysis shows
that, unlike many other exponentiation based protocols, security of the
protocol goes beyond the level of security provided by (DDH) assumption and
intractability of Discrete Logarithm Problem (DLP). Actually, security of the
protocol completely transcends the reliance on the DLP in the sense that
breaking the DLP does not mean breaking the protocol. Complexity of brute force
attack on the protocol is equivalent to exhaustive search for the secret key
A New Post-Quantum Key Agreement Protocol and Derived Cryptosystem Based on Rectangular Matrices
In this paper, we present an original algorithm to generate session keys and a subsequent generalized ElGamal-type cryptosystem. The scheme presented here has been designed to prevent both linear and brute force attacks using rectangular matrices and to achieve high complexity. Our algorithm includes a new generalized Diffie-Hellmann scheme based on rectangular matrices and polynomial field operations. Two variants are presented, the first with a double exchange between the parties and the second with a single exchange, thus speeding up the generation of session keys
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
Legacy encryption systems depend on sharing a key (public or private) among
the peers involved in exchanging an encrypted message. However, this approach
poses privacy concerns. Especially with popular cloud services, the control
over the privacy of the sensitive data is lost. Even when the keys are not
shared, the encrypted material is shared with a third party that does not
necessarily need to access the content. Moreover, untrusted servers, providers,
and cloud operators can keep identifying elements of users long after users end
the relationship with the services. Indeed, Homomorphic Encryption (HE), a
special kind of encryption scheme, can address these concerns as it allows any
third party to operate on the encrypted data without decrypting it in advance.
Although this extremely useful feature of the HE scheme has been known for over
30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE)
scheme, which allows any computable function to perform on the encrypted data,
was introduced by Craig Gentry in 2009. Even though this was a major
achievement, different implementations so far demonstrated that FHE still needs
to be improved significantly to be practical on every platform. First, we
present the basics of HE and the details of the well-known Partially
Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which
are important pillars of achieving FHE. Then, the main FHE families, which have
become the base for the other follow-up FHE schemes are presented. Furthermore,
the implementations and recent improvements in Gentry-type FHE schemes are also
surveyed. Finally, further research directions are discussed. This survey is
intended to give a clear knowledge and foundation to researchers and
practitioners interested in knowing, applying, as well as extending the state
of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the
survey that is being submitted to ACM CSUR and has been uploaded to arXiv for
feedback from stakeholder
Efficient Computation and FPGA implementation of Fully Homomorphic Encryption with Cloud Computing Significance
Homomorphic Encryption provides unique security solution for cloud computing. It ensures not only that data in cloud have confidentiality but also that data processing by cloud server does not compromise data privacy. The Fully Homomorphic Encryption (FHE) scheme proposed by Lopez-Alt, Tromer, and Vaikuntanathan (LTV), also known as NTRU(Nth degree truncated polynomial ring) based method, is considered one of the most important FHE methods suitable for practical implementation. In this thesis, an efficient algorithm and architecture for LTV Fully Homomorphic Encryption is proposed. Conventional linear feedback shift register (LFSR) structure is expanded and modified for performing the truncated polynomial ring multiplication in LTV scheme in parallel. Novel and efficient modular multiplier, modular adder and modular subtractor are proposed to support high speed processing of LFSR operations. In addition, a family of special moduli are selected for high speed computation of modular operations. Though the area keeps the complexity of O(Nn^2) with no advantage in circuit level. The proposed architecture effectively reduces the time complexity from O(N log N) to linear time, O(N), compared to the best existing works. An FPGA implementation of the proposed architecture for LTV FHE is achieved and demonstrated. An elaborate comparison of the existing methods and the proposed work is presented, which shows the proposed work gains significant speed up over existing works
(In)Security of an Efficient Fingerprinting Scheme with Symmetric and Commutative Encryption of IWDW 2005
We analyze the security of a fingerprinting scheme proposed at IWDW 2005. We show two results, namely that this scheme (1) does riot provide seller security: a dishonest buyer can repudiate the fact that, he redistributed a content, and (2) does riot, provide buyer security: a buyer can be framed by a malicious seller
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