Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

Unconditionally secure disjointness tests for private datasets

We present two unconditional secure protocols for private set disjointness tests. In order to provide intuition of our protocols, we give a naive example that applies Sylvester matrices. Unfortunately, this simple construction is insecure as it reveals information about the intersection cardinality. More specifically, it discloses its lower bound. By using the Lagrange interpolation, we provide a protocol for the honest-but-curious case without revealing any additional information. Finally, we describe a protocol that is secure against malicious adversaries. In this protocol, a verification test is applied to detect misbehaving participants. Both protocols require O(1) rounds of communication. Our protocols are more efficient than the previous protocols in terms of communication and computation overhead. Unlike previous protocols whose security relies on computational assumptions, our protocols provide information theoretic security. To our knowledge, our protocols are the first ones that have been designed without a generic secure function evaluation. More important, they are the most efficient protocols for private disjointness tests in the malicious adversary case.

Generalized IBE in the exponent-inversion framework

The purpose of this chapter is to provide an abstraction for the class of Exponent-Inversion IBE exemplified by the [Bscr ][Bscr ]2 and [Sscr ][Kscr ] schemes, and, on the basis of that abstraction, to show that those schemes do support interesting and useful extensions such as HIBE and ABE. Our results narrow, if not entirely close, the “flexibility gap” between the Exponent-Inversion and Commutative-Blinding IBE concepts.

Active security in multiparty computation over black-box groups

Most previous work on unconditionally secure multiparty computation has focused on computing over a finite field (or ring). Multiparty computation over other algebraic structures has not received much attention, but is an interesting topic whose study may provide new and improved tools for certain applications. At CRYPTO 2007, Desmedt et al introduced a construction for a passive-secure multiparty multiplication protocol for black-box groups, reducing it to a certain graph coloring problem, leaving as an open problem to achieve security against active attacks. We present the first n-party protocol for unconditionally secure multiparty computation over a black-box group which is secure under an active attack model, tolerating any adversary structure Δ satisfying the Q 3 property (in which no union of three subsets from Δ covers the whole player set), which is known to be necessary for achieving security in the active setting. Our protocol uses Maurer’s Verifiable Secret Sharing (VSS) but preserves the essential simplicity of the graph-based approach of Desmedt et al, which avoids each shareholder having to rerun the full VSS protocol after each local computation. A corollary of our result is a new active-secure protocol for general multiparty computation of an arbitrary Boolean circuit.

NTRUCCA : how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model

NTRUEncrypt is a fast and practical lattice-based public-key encryption scheme, which has been standardized by IEEE, but until recently, its security analysis relied only on heuristic arguments. Recently, Stehlé and Steinfeld showed that a slight variant (that we call pNE) could be proven to be secure under chosen-plaintext attack (IND-CPA), assuming the hardness of worst-case problems in ideal lattices. We present a variant of pNE called NTRUCCA, that is IND-CCA2 secure in the standard model assuming the hardness of worst-case problems in ideal lattices, and only incurs a constant factor overhead in ciphertext and key length over the pNE scheme. To our knowledge, our result gives the first IND-CCA2 secure variant of NTRUEncrypt in the standard model, based on standard cryptographic assumptions. As an intermediate step, we present a construction for an All-But-One (ABO) lossy trapdoor function from pNE, which may be of independent interest. Our scheme uses the lossy trapdoor function framework of Peikert and Waters, which we generalize to the case of (k − 1)-of-k-correlated input distributions.

Identity-based signcryption

The notion of identity-based IB cryptography was proposed by Shamir [177] as a specialization of public key PK cryptography which dispensed with the need for cumbersome directories, certificates, and revocation lists.

Analysis of bilinear pairing-based accumulator for identity escrowing

An accumulator based on bilinear pairings was proposed at CT-RSA'05. Here, it is first demonstrated that the security model proposed by Lan Nguyen does lead to a cryptographic accumulator that is not collision resistant. Secondly, it is shown that collision-resistance can be provided by updating the adversary model appropriately. Finally, an improvement on Nguyen's identity escrow scheme, with membership revocation based on the accumulator, by removing the trusted third party is proposed.

Parallel Signcryption

The primary motivation for signcryption was the gain in efficiency when both encryption and signing need to be performed. These two cryptographic operations may be done sequentially either by first encrypt and then sign (EtS) or alternatively, by first sign and then encrypt (StE). Further gains in efficiency can be achieved if encryption and signature are carried out in parallel (E&S). More importantly, however, is that these efficiency gains are complemented by gains in security, i.e., we may use relative weak encryption and signature schemes in order to obtain a “stronger” signcryption scheme. The reader is referred to Chaps. 2 and 3 for a discussion of the different “strengths” of security model (e.g., outsider vs. insider adversaries, two-user vs. multi-user setting).

Crypto topics and applications II

In this chapter we continue the exposition of crypto topics that was begun in the previous chapter. This chapter covers secret sharing, threshold cryptography, signature schemes, and finally quantum key distribution and quantum cryptography. As in the previous chapter, we have focused only on the essentials of each topic. We have selected in the bibliography a list of representative items, which can be consulted for further details. First we give a synopsis of the topics that are discussed in this chapter. Secret sharing is concerned with the problem of how to distribute a secret among a group of participating individuals, or entities, so that only predesignated collections of individuals are able to recreate the secret by collectively combining the parts of the secret that were allocated to them. There are numerous applications of secret-sharing schemes in practice. One example of secret sharing occurs in banking. For instance, the combination to a vault may be distributed in such a way that only specified collections of employees can open the vault by pooling their portions of the combination. In this way the authority to initiate an action, e.g., the opening of a bank vault, is divided for the purposes of providing security and for added functionality, such as auditing, if required. Threshold cryptography is a relatively recently studied area of cryptography. It deals with situations where the authority to initiate or perform cryptographic operations is distributed among a group of individuals. Many of the standard operations of single-user cryptography have counterparts in threshold cryptography. Signature schemes deal with the problem of generating and verifying electronic) signatures for documents.Asubclass of signature schemes is concerned with the shared-generation and the sharedverification of signatures, where a collaborating group of individuals are required to perform these actions. A new paradigm of security has recently been introduced into cryptography with the emergence of the ideas of quantum key distribution and quantum cryptography. While classical cryptography employs various mathematical techniques to restrict eavesdroppers from learning the contents of encrypted messages, in quantum cryptography the information is protected by the laws of physics.

A new human identification protocol and Coppersmith's baby-step giant-step algorithm

We propose a new protocol providing cryptographically secure authentication to unaided humans against passive adversaries. We also propose a new generic passive attack on human identification protocols. The attack is an application of Coppersmith’s baby-step giant-step algorithm on human identification protcols. Under this attack, the achievable security of some of the best candidates for human identification protocols in the literature is further reduced. We show that our protocol preserves similar usability while achieves better security than these protocols. A comprehensive security analysis is provided which suggests parameters guaranteeing desired levels of security.

Certified pseudonyms colligated with master secret key

A pseudonym provides anonymity by protecting the identity of a legitimate user. A user with a pseudonym can interact with an unknown entity and be confident that his/her identity is secret even if the other entity is dishonest. In this work, we present a system that allows users to create pseudonyms from a trusted master public-secret key pair. The proposed system is based on the intractability of factoring and finding square roots of a quadratic residue modulo a composite number, where the composite number is a product of two large primes. Our proposal is different from previously published pseudonym systems, as in addition to standard notion of protecting privacy of an user, our system offers colligation between seemingly independent pseudonyms. This new property when combined with a trusted platform that stores a master secret key is extremely beneficial to an user as it offers a convenient way to generate a large number of pseudonyms using relatively small storage.

Multi-party computation with omnipresent adversary

Secure multi-party computation (MPC) protocols enable a set of n mutually distrusting participants P 1, ..., P n , each with their own private input x i , to compute a function Y = F(x 1, ..., x n ), such that at the end of the protocol, all participants learn the correct value of Y, while secrecy of the private inputs is maintained. Classical results in the unconditionally secure MPC indicate that in the presence of an active adversary, every function can be computed if and only if the number of corrupted participants, t a , is smaller than n/3. Relaxing the requirement of perfect secrecy and utilizing broadcast channels, one can improve this bound to t a  < n/2. All existing MPC protocols assume that uncorrupted participants are truly honest, i.e., they are not even curious in learning other participant secret inputs. Based on this assumption, some MPC protocols are designed in such a way that after elimination of all misbehaving participants, the remaining ones learn all information in the system. This is not consistent with maintaining privacy of the participant inputs. Furthermore, an improvement of the classical results given by Fitzi, Hirt, and Maurer indicates that in addition to t a actively corrupted participants, the adversary may simultaneously corrupt some participants passively. This is in contrast to the assumption that participants who are not corrupted by an active adversary are truly honest. This paper examines the privacy of MPC protocols, and introduces the notion of an omnipresent adversary, which cannot be eliminated from the protocol. The omnipresent adversary can be either a passive, an active or a mixed one. We assume that up to a minority of participants who are not corrupted by an active adversary can be corrupted passively, with the restriction that at any time, the number of corrupted participants does not exceed a predetermined threshold. We will also show that the existence of a t-resilient protocol for a group of n participants, implies the existence of a t’-private protocol for a group of n′ participants. That is, the elimination of misbehaving participants from a t-resilient protocol leads to the decomposition of the protocol. Our adversary model stipulates that a MPC protocol never operates with a set of truly honest participants (which is a more realistic scenario). Therefore, privacy of all participants who properly follow the protocol will be maintained. We present a novel disqualification protocol to avoid a loss of privacy of participants who properly follow the protocol.

A fair e-tendering protocol

Implementation of an electronic tendering (e-tendering) systems requires careful attention to the needs of the system and its various participants. Fairness in an e-tendering is of utmost importance. Current proposals and implementations do not provide fairness and thus, are vulnerable to collusion and favourism. Dishonest participants, either the principal or tenderer may collude to alter or view competing tenders which would give the favoured tenderer a greater chance of winning the contract. This paper proposes an e-tendering system that is secure and fair to all participants. We employ the techniques of anonymous token system along with signed commitment approach to achieve a publicly verifiable fair e-tendering protocol. We also provide an analysis of the protocol that confirms the security of our proposal against security goals for an e-tendering system.

MöBIUS-α commutative functions and partially coincident functions

The M¨obius transform of Boolean functions is often involved in cryptographic design and analysis. As studied previously, a Boolean function f is said to be coincident if it is identical with its M¨obius transform fμ, i.e., f = fμ...

An algebraic analysis of trivium ciphers based on the boolean satisfiability problem

Trivium is a stream cipher candidate of the eStream project. It has successfully moved into phase three of the selection process under the hardware category. No attacks faster than the exhaustive search have so far been reported on Trivium. Bivium-A and Bivium-B are simplified versions of Trivium that are built on the same design principles but with two registers. The simplified design is useful in investigating Trivium type ciphers with a reduced complexity and provides insight into effective attacks which could be extended to Trivium. This paper focuses on an algebraic analysis which uses the boolean satisfiability problem in propositional logic. For reduced variants of the cipher, this analysis recovers the internal state with a minimal amount of keystream observations.