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.

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.

Spreadsheet Conditional Formatting Illuminates Investigations into Modular Arithmetic

Modular arithmetic has often been regarded as something of a mathematical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digital security systems such as RSA, this important branch of mathematics is now considered essential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound d 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

An efficient eAuction potocol

A secure protocol for electronic, sealed-bid, single item auctions is presented. The protocol caters to both first and second price (Vickrey) auctions and provides full price flexibility. Both computational and communication cost are linear with the number of bidders and utilize only standard cryptographic primitives. The protocol strictly divides knowledge of the bidder's identity and their actual bids between, respectively, a registration authority and an auctioneer, who are assumed not to collude but may be separately corrupt. This assures strong bidder-anonymity, though only weak bid privacy. The protocol is structured in two phases, each involving only off-line communication. Registration, requiring the use of the public key infrastructure, is simultaneous with hash-sealed bid-commitment and generates a receipt to the bidder containing a pseudonym. This phase is followed by encrypted bid-submission. Both phases involve the registration authority acting as a communication conduit but the actual message size is quite small. It is argued that this structure guarantees non-repudiation by both the winner and the auctioneer. Second price correctness is enforced either by observing the absence of registration of the claimed second-price bid or, where registered but lower than the actual second price, is subject to cooperation by the second price bidder - presumably motivated through self-interest. The use of the registration authority in other contexts is also considered with a view to developing an architecture for efficient secure multiparty transactions

Higher order universal one-way hash functions from the subset sum assumption

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgård domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs. We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log m). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgård extender to the subset sum compression function with ‘extension factor’ k+1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k+1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

Efficient one-time proxy signatures

One-time proxy signatures are one-time signatures for which a primary signer can delegate his or her signing capability to a proxy signer. In this work we propose two one-time proxy signature schemes with different security properties. Unlike other existing one-time proxy signatures that are constructed from public key cryptography, our proposed schemes are based one-way functions without trapdoors and so they inherit the communication and computation efficiency from the traditional one-time signatures. Although from a verifier point of view, signatures generated by the proxy are indistinguishable from those created by the primary signer, a trusted authority can be equipped with an algorithm that allows the authority to settle disputes between the signers. In our constructions, we use a combination of one-time signatures, oblivious transfer protocols and certain combinatorial objects. We characterise these new combinatorial objects and present constructions for them.

Efficient extension of standard Schnorr/RSA signatures into Universal Designated-Verifier Signatures

Universal Designated-Verifier Signature (UDVS) schemes are digital signature schemes with additional functionality which allows any holder of a signature to designate the signature to any desired designated-verifier such that the designated-verifier can verify that the message was signed by the signer, but is unable to convince anyone else of this fact. Since UDVS schemes reduce to standard signatures when no verifier designation is performed, it is natural to ask how to extend the classical Schnorr or RSA signature schemes into UDVS schemes, so that the existing key generation and signing implementation infrastructure for these schemes can be used without modification. We show how this can be efficiently achieved, and provide proofs of security for our schemes in the random oracle model.

Security issues for future intelligent transport systems

Cooperative Intelligent Transportation Systems (C-ITS) allow in-vehicle systems, and ultimately the driver, to enhance their awareness of their surroundings by enabling communication between vehicles and road infrastructure. C-ITS are widely considered as the next major step in driving assistance systems, aiming at increasing safety, comfort and mobility for drivers. However, any communicating systems are subjected to security threats. A key component for providing secure communications at a large scale is a Public Key Infrastructure (PKI). Due to the safety-critical nature of Vehicle-to-Vehicle (V2V) communications, a C-ITS PKI has functional, performance and scalability requirements that differ from traditional non-automotive environments. This paper identifies and defines the key functional and security requirements for C-ITS PKI systems and analyses proposed C-ITS PKI standards against these requirements. In particular, the proposed US and European C-ITS PKI systems are identified as being too complex and not scalable. The paper also highlights various privacy, security and scalability concerns that should be considered for a secure C-ITS PKI solution in the Australian transport landscape.

On the leakage resilience of secure channel establishment

Secure communication channels are typically constructed from an authenticated key exchange (AKE) protocol, which authenticates the communicating parties and establishes shared secret keys, and a secure data transmission layer, which uses the secret keys to encrypt data. We address the partial leakage of communicating parties' long-term secret keys due to various side-channel attacks, and the partial leakage of plaintext due to data compression. Both issues can negatively affect the security of channel establishment and data transmission. In this work, we advance the modelling of security for AKE protocols by considering more granular partial leakage of parties' long-term secrets. We present generic and concrete constructions of two-pass leakage-resilient key exchange protocols that are secure in the proposed security models. We also examine two techniques--heuristic separation of secrets and fixed-dictionary compression--for enabling compression while protecting high-value secrets.

Algebraic Cryptanalysis of CTRU Cryptosystem

CTRU, a public key cryptosystem was proposed by Gaborit, Ohler and Sole. It is analogue of NTRU, the ring of integers replaced by the ring of polynomials $\mathbb{F}_2[T]$ . It attracted attention as the attacks based on either LLL algorithm or the Chinese Remainder Theorem are avoided on it, which is most common on NTRU. In this paper we presents a polynomial-time algorithm that breaks CTRU for all recommended parameter choices that were derived to make CTRU secure against popov normal form attack. The paper shows if we ascertain the constraints for perfect decryption then either plaintext or private key can be achieved by polynomial time linear algebra attack.

From Selective-ID to Full-ID IBS without Random Oracles

Since its induction, the selective-identity (sID) model for identity-based cryptosystems and its relationship with various other notions of security has been extensively studied. As a result, it is a general consensus that the sID model is much weaker than the full-identity (ID) model. In this paper, we study the sID model for the particular case of identity-based signatures (IBS). The main focus is on the problem of constructing an ID-secure IBS given an sID-secure IBS without using random oracles-the so-called standard model-and with reasonable security degradation. We accomplish this by devising a generic construction which uses as black-box: i) a chameleon hash function and ii) a weakly-secure public-key signature. We argue that the resulting IBS is ID-secure but with a tightness gap of O(q(s)), where q(s) is the upper bound on the number of signature queries that the adversary is allowed to make. To the best of our knowledge, this is the first attempt at such a generic construction.

基于加同态公钥密码体制的匿名数字指纹方案

提出了一种基于加同态公钥密码算法的匿名数字指纹方案，并给出了具有匿名功能的公钥和私钥对的具体构造方法，从而使该匿名指纹方案在发现盗版的情况下，销售商不需要第三方的帮助就能鉴别出数字多媒体作品的非法分发者，解决版权纠纷时也不需要购买者参与并提供相关的秘密信息，从而达到实现两方审判的目的．分析结果表明，该方案具有用户匿名及不可关联、销售商的可保证安全性和用户的可保证安全性等特点．

纯公钥模型下对NP语言的高效并发零知识证明系统

提出了一种从3轮公开掷币的对任何NP语言的诚实验证者零知识证明系统到纯公钥模型下4轮f轮最优）对同一语言的具有并发合理性的并发零知识证明系统．该转化方法有如下优点：1）它只引起D（1）（常数个）额外的模指数运算，相比DiCrescenzo等人在ICALP05上提出的需要qn）个额外的模指数运算的转化方法孩系统在效率上有着本质上的提高，而所需的困难性假设不变；2）在离散对数假设下，该转化方法产生一个完美零知识证明系统．注意到DiCrescenzo等人提出的系统只具有计算零知识性质．该转化方法依赖于一个特殊的对承诺中的离散对数的3轮诚实验证者零知识的证明系统．构造了两个基于不同承诺方案的只需要常数个模指数运算的系统这种系统可能有着独立价值．