Chosen-ciphertext security from subset sum

We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012

Normal Elliptic Bases and Torus-Based Cryptography

We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements, to a small fixed overhead and to $m$ $\phi(n)$-tuples of $F_q$ elements, in quasi-linear time in $\log q$. This improves upon previously known algorithms, which all have a quasi-quadratic complexity. As a result, the cost of the encoding phase is now negligible in Diffie-Hellman cryptographic schemes

Highly Efficient Key Exchange Protocols with Optimal Tightness -- Enabling real-world deployments with theoretically sound parameters

In this paper we give nearly tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols, which are extremely simple and efficient. Unlike previous approaches, the combination of nearly tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner, i.e., according to the bounds of the reductions. Specifically, our reductions have a security loss which is only linear in the number of users $\mu$ and constant in the number of sessions per user $\ell$. This is much better than most other key exchange proofs which are typically quadratic in the product $\mu \ell$. Combined with the simplicity of our protocols, this implies that our protocols are more efficient than the state of the art when soundly instantiated. We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions

The Twin Diffie-Hellman Problem and Applications

We propose a new computational problem called the \emph{twin Diffie-Hellman problem}. This problem is closely related to the usual (computational) Diffie-Hellman problem and can be used in many of the same cryptographic constructions that are based on the Diffie-Hellman problem. Moreover, the twin Diffie-Hellman problem is at least as hard as the ordinary Diffie-Hellman problem. However, we are able to show that the twin Diffie-Hellman problem remains hard, even in the presence of a decision oracle that recognizes solutions to the problem --- this is a feature not enjoyed by the Diffie-Hellman problem in general. Specifically, we show how to build a certain ``trapdoor test\u27\u27 that allows us to effectively answer decision oracle queries for the twin Diffie-Hellman problem without knowing any of the corresponding discrete logarithms. Our new techniques have many applications. As one such application, we present a new variant of ElGamal encryption with very short ciphertexts, and with a very simple and tight security proof, in the random oracle model, under the assumption that the ordinary Diffie-Hellman problem is hard. We present several other applications as well, including: a new variant of Diffie and Hellman\u27s non-interactive key exchange protocol; a new variant of Cramer-Shoup encryption, with a very simple proof in the standard model; a new variant of Boneh-Franklin identity-based encryption, with very short ciphertexts; a more robust version of a password-authenticated key exchange protocol of Abdalla and Pointcheval

Highly Efficient Key Exchange Protocols with Optimal Tightness: Enabling real-world deployments with theoretically sound parameters

In this paper we give nearly-tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols which are extremely simple and efficient. Unlike previous approaches, the combination of nearly-tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner. Our reductions have only a linear loss in the number of users, implying that our protocols are more efficient than the state of the art when instantiated with theoretically sound parameters. We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions

Sufficient condition for ephemeral key-leakage resilient tripartite key exchange

17th Australasian Conference on Information Security and Privacy, ACISP 2012; Wollongong, NSW; Australia; 9 July 2012 through 11 July 2012Tripartite (Diffie-Hellman) Key Exchange (3KE), introduced by Joux (ANTS-IV 2000), represents today the only known class of group key exchange protocols, in which computation of unauthenticated session keys requires one round and proceeds with minimal computation and communication overhead. The first one-round authenticated 3KE version that preserved the unique efficiency properties of the original protocol and strengthened its security towards resilience against leakage of ephemeral (session-dependent) secrets was proposed recently by Manulis, Suzuki, and Ustaoglu (ICISC 2009). In this work we explore sufficient conditions for building such protocols. We define a set of admissible polynomials and show how their construction generically implies 3KE protocols with the desired security and efficiency properties. Our result generalizes the previous 3KE protocol and gives rise to many new authenticated constructions, all of which enjoy forward secrecy and resilience to ephemeral key-leakage under the gap Bilinear Diffie-Hellman assumption in the random oracle model. © 2012 Springer-Verlag

Group Action Key Encapsulation and Non-Interactive Key Exchange in the QROM

In the context of quantum-resistant cryptography, cryptographic group actions offer an abstraction of isogeny-based cryptography in the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) setting. In this work, we revisit the security of two previously proposed natural protocols: the Group Action Hashed ElGamal key encapsulation mechanism (GA-HEG KEM) and the Group Action Hashed Diffie-Hellman non-interactive key-exchange (GA-HDH NIKE) protocol. The latter protocol has already been considered to be used in practical protocols such as Post-Quantum WireGuard (S&P \u2721) and OPTLS (CCS \u2720). We prove that active security of the two protocols in the Quantum Random Oracle Model (QROM) inherently relies on very strong variants of the Group Action Strong CDH problem, where the adversary is given arbitrary quantum access to a DDH oracle. That is, quantum accessible Strong CDH assumptions are not only sufficient but also necessary to prove active security of the GA-HEG KEM and the GA-HDH NIKE protocols. Furthermore, we propose variants of the protocols with QROM security from the classical Strong CDH assumption, i.e., CDH with classical access to the DDH oracle. Our first variant uses key confirmation and can therefore only be applied in the KEM setting. Our second but considerably less efficient variant is based on the twinning technique by Cash et al. (EUROCRYPT \u2708) and in particular yields the first actively secure isogeny-based NIKE with QROM security from the standard CDH assumption

On Designated Verifier Signature Schemes

Designated verifier signature schemes allow a signer to convince only the designated verifier that a signed message is authentic. We define attack models on the unforgeability property of such schemes and analyze relationships among the models. We show that the no-message model, where an adversary is given only public keys, is equivalent to the model, where an adversary has also oracle access to the verification algorithm. We also show a separation between the no-message model and the chosen-message model, where an adversary has access to the signing algorithm. Furthermore, we present a modification of the Yang-Liao designated verifier signature scheme and prove its security. The security of the modified scheme is based on the computational Diffie-Hellman problem, while the original scheme requires strong Diffie-Hellman assumption

CCA secure ElGamal encryption over an integer group where ICDH assumption holds

In order to prove the ElGamal CCA (Chosen Ciphertext Attack) security in the random oracle model, it is necessary to use the group (i.e., ICDH group) where ICDH assumption holds. Until now, only bilinear group where ICDH assumption is equivalent to CDH assumption has been known as the ICDH group. In this paper, we introduce another ICDH group in which ICDH assumption holds under the RSA assumption. Based on this group, we propose the CCA secure ElGamal encryption. And we describe the possibility to speed up decryption by reducing CRT (Chinese Remainder Theorem) exponents in CCA secure ElGamal

Theory and Applications of Outsider Anonymity in Broadcast Encryption

Broadcast Encryption (BE) allows efficient one-to-many secret communication of data over a broadcast channel. In the standard setting of BE, information about receivers is transmitted in the clear together with ciphertexts. This could be a serious violation of recipient privacy since the identities of the users authorized to access the secret content in certain broadcast scenarios are as sensitive as the content itself. Anonymous Broadcast Encryption (AnoBe) prevents this leakage of recipient identities from ciphertexts but at a cost of a linear lower bound (in the number of receivers) on the length of ciphertexts. A linear ciphertext length is a highly undesirable bottleneck in any large-scale broadcast application. In this thesis, we propose a less stringent yet very meaningful notion of anonymity for anonymous broadcast encryption called Outsider-Anonymous Broadcast Encryption (oABE) that allows the creation of ciphertexts that are sublinear in the number of receivers. We construct several oABE schemes with varying security guarantees and levels of efficiency. We also present two very interesting cryptographic applications afforded by the efficiency of our oABE schemes. The first is Broadcast Steganography (BS), the extension of the state of the art setting of point-to-point steganography to the multi-recipient setting. The second is Oblivious Group Storage (OGS), the introduction of fine-grained data access control policies to the setting of multi-client oblivious cloud storage protocols