Li, Ling, Xing, and Yeo (LLXY) have proposed a code-based encryption scheme based on factoring in finite fields. The security of the scheme relies on both the decoding problem for (q – 1)-ary codes, and the Bounded Distance Decoding problem for the ℓ-norm in a family of lattices. On the negative side, we describe a Chosen Ciphertext Attack that breaks the claimed CCA protection proposed by LLXY. We also extend a previous cryptanalysis by Lapiha using decoding attacks, and argue that the May-Ozerov information set decoding attack is the most powerful decoding attack on the scheme. On the positive side, we streamline the description of the scheme and give simple algorithms to generate the public keys. We also give a Niederreiter version of the scheme that has smaller ciphertexts, and show how to correctly obtain a CCA secure Key Encapsulation Mechanism by using standard techniques.

Abstract An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of ‘hard supersingular curves’ that is equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell $-isogeny graph, which does not reveal the endomorphism ring, or a path to a curve of known endomorphism ring. Such a hash function would open up interesting cryptographic applications. In this paper, we document a number of (thus far) failed attempts to solve this problem, in the hope that we may spur further research, and shed light on the challenges and obstacles to this endeavour. The mathematical approaches contained in this article include: (i) iterative root-finding for the supersingular polynomial; (ii) gcd’s of specialized modular polynomials; (iii) using division polynomials to create small systems of equations; (iv) taking random walks in the isogeny graph of abelian surfaces, and applying Kummer surfaces and (v) using quantum random walks.

Searchable Encryption (SE) is a technique that allows Cloud Service Providers to search over encrypted datasets without learning the content of queries and records. In recent years, many SE schemes have been proposed to protect outsourced data. However, most of them leak sensitive information, from which attackers could still infer the content of queries and records by mounting leakage-based inference attacks, such as the count attack and file-injection attack . In this work, first we define the leakage in searchable encrypted databases and analyse how the leakage is leveraged in existing leakage-based attacks. Second, we propose a Privacy-preserving Multi-cloud based dynamic symmetric SE scheme for relational Database ( P-McDb ). P-McDb has minimal leakage, which not only ensures confidentiality of queries and records but also protects the search, intersection, and size patterns. Moreover, P-McDb ensures both forward and backward privacy of the database. Thus, P-McDb could resist existing leakage-based attacks, e.g., active file/record-injection attacks. We give security definition and analysis to show how P-McDb hides the aforementioned patterns. Finally, we implemented a prototype of P-McDb and tested it using the TPC-H benchmark dataset. Our evaluation results show that users can get the required records in 2.16 s when searching over 4.1 million records.

Most recent theoretical literature on program obfuscation is based on notions like virtual black box (VBB) obfuscation and indistinguishability obfuscation (iO). These notions are very strong and are hard to satisfy. Further, they offer far more protection than is typically required in practical applications. On the other hand, the security notions introduced by software security researchers are suitable for practical designs but are not formal or precise enough to enable researchers to provide a quantitative security assurance. Hence, in this paper, we introduce a new formalism for practical program obfuscation that still allows rigorous security proofs. We believe our formalism will make it easier to analyse the security of obfuscation schemes. To show the flexibility and power of our formalism, we give a number of examples. Moreover, we explain the close relationship between our formalism and the task of providing obfuscation challenges.

We present signature schemes whose security relies on computational assumptions relating to isogeny graphs of supersingular elliptic curves. We give two schemes, both of them based on interactive identification protocols. The first identification protocol is due to De Feo, Jao and Plût. The second one, and the main contribution of the paper, makes novel use of an algorithm of Kohel, Lauter, Petit and Tignol for the quaternion version of the \(\ell \) -isogeny problem, for which we provide a more complete description and analysis, and is based on a more standard and potentially stronger computational problem. Both identification protocols lead to signatures that are existentially unforgeable under chosen message attacks in the random oracle model using the well-known Fiat-Shamir transform, and in the quantum random oracle model using another transform due to Unruh. A version of the first signature scheme was independently published by Yoo, Azarderakhsh, Jalali, Jao and Soukharev. This is the full version of a paper published at ASIACRYPT 2017.

Searchable Symmetric Encryption (SSE) allows users to execute encrypted queries over encrypted databases. A large number of SSE schemes have been proposed in the literature. However, most of them leak a significant amount of information that could lead to inference attacks. In this work, we propose an SSE scheme for a Privacy-preserving Multi-cloud encrypted Database (P-McDb), which aims at preventing inference attacks. P-McDb allows users to execute SQL-like queries in an efficient sub-linear manner without leaking search, access and size patterns. We have implemented a prototype of P-McDb and show its practical efficiency.

In this paper, we discuss some applications of the pairing inversion problem and outline some potential approaches for solving it. Our analysis of these approaches gives further evidence that pairing inversion is a difficult problem.