Public-Key encryption resilient against linear Related-Key attacks revisited

Wee (PKC'12) proposed a generic public-key encryption scheme in the setting of related-key attacks. Bellare, Paterson and Thomson (Asiacrypt'12) provided a framework enabling related-key attack (RKA) secure cryptographic primitives for a class of non-linear related-key derivation functions. However, in both of their constructions, the instantiations to achieve the full (not weak) RKA security are given under the scenario regarding the private key composed of single element. In other words, each element of the private key shares the same modification. However, this is impractical in real world. In this paper, we concentrate on the security of public-key encryption schemes under linear related-key attacks in the setting of multielement private keys (that is, the private key is composed of more than one element), where an adversary is allowed to tamper any part of this private key stored in a hardware device, and subsequently observes the outcome of a public key encryption system under this targeted modified private key. We define the security model for RKA secure public-key encryption schemes as chosen-cipher text and related-key attack (CC-RKA) security, which means that a public-key encryption scheme remains secure even when an adversary is allowed to issue the decryption oracle on linear shifts of any component of the private key. After that, we present a detailed public key encryption schemes with the private key formed of several elements, of which the CC-RKA security is under the decisional BDH assumption in the standard model

Security Against Related Randomness Attacks via Reconstructive Extractors

Abstract. This paper revisits related randomness attacks against public key encryption schemes as introduced by Paterson, Schuldt and Sibborn (PKC 2014). We present a general transform achieving security for pub-lic key encryption in the related randomness setting using as input any secure public key encryption scheme in combination with an auxiliary-input reconstructive extractor. Specifically, we achieve security in the function-vector model introduced by Paterson et al., obtaining the first constructions providing CCA security in this setting. We consider in-stantiations of our transform using the Goldreich-Levin extractor; these outperform the previous constructions in terms of public-key size and reduction tightness, as well as enjoying CCA security. Finally, we also point out that our approach leads to an elegant construction for Corre-lation Input Secure hash functions, which have proven to be a versatile tool in diverse areas of cryptography

Hardware Implementation of a Polar Code-based Public Key Cryptosystem

In recent years, there have been many studies on quantum computing and the construction of quantum computers which are capable of breaking conventional number theory-based public key cryptosystems. Therefore, in the not-too-distant future, we need the public key cryptosystems that withstand against the attacks executed by quantum computers, so-called post-quantum cryptosystems. A public key cryptosystem based on polar codes (PKC-PC) has recently been introduced whose security depends on the difficulty of solving the general decoding problem of polar code. In this paper, we first implement the encryption, key generation and decryption algorithms of PKC-PC on Raspberry Pi3. Then, to evaluate its performance, we have measured several related parameters such as execution time, energy consumption, memory consumption and CPU utilization. All these metrics are investigated for encryption/decryption algorithms of PKC-PC with various parameters of polar codes. In the next step, the investigated parameters are compared to the implemented McEliece public key cryptosystem. Analyses of such results show that the execution time of encryption/decryption as well as the energy and memory consumption of PKC-PC is shorter than the McEliece cryptosystem.Comment: 19 pages, 15 figure

Efficient Fully Homomorphic Encryption from (Standard) LWE

A fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, m, into an encryption of any (efficient) function of that message, f(m), without knowing the secret key. We present a leveled FHE scheme that is based solely on the (standard) learning with errors (LWE) assumption. (Leveled FHE schemes are initialized with a bound on the maximal evaluation depth. However, this restriction can be removed by assuming “weak circular security.”) Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems” on arbitrary lattices. Our construction improves on previous works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional assumptions. Our scheme has very short ciphertexts, and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k·polylog(k)+log |DB| bits per single-bit query, in order to achieve security against 2k-time adversaries (based on the best known attacks against our underlying assumptions). Key words. cryptology, public-key encryption, fully homomorphic encryption, learning with errors, private information retrieva

Public Key Encryption with Secure Key Leasing

We introduce the notion of public key encryption with secure key leasing (PKE-SKL). Our notion supports the leasing of decryption keys so that a leased key achieves the decryption functionality but comes with the guarantee that if the quantum decryption key returned by a user passes a validity test, then the user has lost the ability to decrypt. Our notion is similar in spirit to the notion of secure software leasing (SSL) introduced by Ananth and La Placa (Eurocrypt 2021) but captures significantly more general adversarial strategies. In more detail, our adversary is not restricted to use an honest evaluation algorithm to run pirated software. Our results can be summarized as follows: 1. Definitions: We introduce the definition of PKE with secure key leasing and formalize security notions. 2. Constructing PKE with Secure Key Leasing: We provide a construction of PKE-SKL by leveraging a PKE scheme that satisfies a new security notion that we call consistent or inconsistent security against key leasing attacks (CoIC-KLA security). We then construct a CoIC-KLA secure PKE scheme using 1-key Ciphertext-Policy Functional Encryption (CPFE) that in turn can be based on any IND-CPA secure PKE scheme. 3. Identity Based Encryption, Attribute Based Encryption and Functional Encryption with Secure Key Leasing: We provide definitions of secure key leasing in the context of advanced encryption schemes such as identity based encryption (IBE), attribute-based encryption (ABE) and functional encryption (FE). Then we provide constructions by combining the above PKE-SKL with standard IBE, ABE and FE schemes.Comment: 68 pages, 4 figures. added related works and a comparison with a concurrent work (2023-04-07

Related Message Attacks to Public Key Encryption Schemes: Relations among Security Notions

Consider a scenario in which an adversary, attacking a certain public key encryption scheme, gains knowledge of several ciphertexts which underlying plaintext are meaningfully related with a given target ciphertext. This kind of related message attack has been proved successful against several public key encryption schemes; widely known is the Franklin-Reiter attack to RSA with low exponent and its subsequent improvement by Coppersmith. However, to the best of our knowledge no formal treatment of these type of attacks has to date been done, and as a result, it has not been rigorously studied which of the ``standard\u27\u27 security notions imply resilience to them. We give formal definitions of several security notions capturing the resistance to this kind of attacks. For passive adversaries we prove that, for the case of indistinguishability, security against related message attacks is equivalent to standard CPA security. On the other hand, one-wayness robust schemes in this sense can be seen as strictly between OW-CPA and IND-CPA secure schemes. Furthermore, we prove that the same holds for active (CCA) adversaries

Certificate-Less Searchable Encryption with a Refreshing Keyword Search

Public Key Encryptions with Keyword Search (PEKS) scheme had been hosted for keeping data security and privacy of outsourced data in a cloud environment. It is also used to provide search operations on encrypted data. Nevertheless, most of the existing PEKS schemes are disposed to key-escrow problems due to the private key of the target users are known by the Key Generating Center (KGC). To improve the key escrow issue in PEKS schemes, the Certificate-Less Public Key Encryptions with Keyword Search (CL-PEKS) scheme has been designed. Meanwhile, the existing CL-PEKS schemes do not consider refreshing keyword searches. Due to this, the cloud server can store search trapdoors for keywords used in the system and can launch keyword guessing attacks. In this research work, we proposed Certificate-Less Searchable Encryption with a Refreshing Keyword Search (CL-SERKS) scheme by attaching date information to the encrypted data and keyword. We demonstrated that our proposed scheme is secure against adaptively chosen keyword attacks against both types of adversaries, where one adversary is given the power to select a random public key as a replacement for the user’s public key whereas another adversary is allowed to learn the system master key in the random oracle model under the Bilinear Diffie-Hellman problem assumption. We evaluated the performance of the proposed scheme in terms of both computational cost and communication cost. Experimental results show that the proposed CL-SERKS scheme has better computational cost during the key generation phase and testing phase than two related schemes. It also has lower communication costs than both related schemes

On the Feasibility of Identity-based Encryption with Equality Test against Insider Attacks

As a generalization of public key encryption with keyword search, public key encryption with equality test was proposed, and identity-based encryption with equality test (IBEET) is its identity-based variant. In IBEET, anyone can check whether two ciphertexts of distinct identities are encryptions of the same plaintext or not using trapdoors. Due to its functionality, IBEET cannot provide any indistinguishability-based security for trapdoor holders. As a variant of IBEET, IBEET against insider attacks (IBEETIA) was proposed, where a token is defined for each identity and is used for encryption, and anyone can check whether two ciphertexts of distinct identities are encryptions of the same plaintext or not without using trapdoors, and an indistinguishability security of IBEETIA was defined. Lee et al. (ACISP 2018) and Duong et al. (ProvSec 2019) proposed a paring-based and a lattice-based constructions, respectively. That is, current concrete IBEETIA schemes are constructed by identity-based encryption (IBE) related complexity assumptions. According to the implication result shown by Boneh et al. (FOCS 2008), IBE is recognized as a strong cryptographic primitive because no black-box construction of IBE from trapdoor permutations exist. However, Emura and Takayasu (IEICE Transactions 2023) demonstrated that symmetric key encryption and pseudo-random permutations are sufficient to construct IBEETIA which is secure in the previous security definition. These results suggest us to explore a condition of IBEETIA that requires to employ IBE-related complexity assumptions. In this paper, we demonstrate a sufficient condition that IBEETIA implies IBE. We define one-wayness against chosen-plaintext/ciphertext attacks for the token generator (OW-TG-CPA/CCA) and for token holders (OW-TH-CPA/CCA), which were not considered in the previous security definition. We show that OW-TG-CPA secure IBEETIA with additional conditions implies OW-CPA secure IBE, and show that Lee et al. and Duong et al. schemes provide the OW-TG-CPA security. On the other hand, we propose a generic construction of OW-TH-CCA secure IBEETIA from public key encryption. Our results suggest a design principle to efficiently construct IBEETIA without employing IBE-related complexity assumptions

Functional Encryption: Deterministic to Randomized Functions from Simple Assumptions

Functional encryption (FE) enables fine-grained control of sensitive data by allowing users to only compute certain functions for which they have a key. The vast majority of work in FE has focused on deterministic functions, but for several applications such as privacy-aware auditing, differentially-private data release, proxy re-encryption, and more, the functionality of interest is more naturally captured by a randomized function. Recently, Goyal et al. (TCC 2015) initiated a formal study of FE for randomized functionalities with security against malicious encrypters, and gave a selectively secure construction from indistinguishability obfuscation. To date, this is the only construction of FE for randomized functionalities in the public-key setting. This stands in stark contrast to FE for deterministic functions which has been realized from a variety of assumptions. Our key contribution in this work is a generic transformation that converts any general-purpose, public-key FE scheme for deterministic functionalities into one that supports randomized functionalities. Our transformation uses the underlying FE scheme in a black-box way and can be instantiated using very standard number-theoretic assumptions (for instance, the DDH and RSA assumptions suffice). When applied to existing FE constructions, we obtain several adaptively-secure, public-key functional encryption schemes for randomized functionalities with security against malicious encrypters from many different assumptions such as concrete assumptions on multilinear maps, indistinguishability obfuscation, and in the bounded-collusion setting, the existence of public-key encryption, together with standard number-theoretic assumptions. Additionally, we introduce a new, stronger definition for malicious security as the existing one falls short of capturing an important class of correlation attacks. In realizing this definition, our compiler combines ideas from disparate domains like related-key security for pseudorandom functions and deterministic encryption in a novel way. We believe that our techniques could be useful in expanding the scope of new variants of functional encryption (e.g., multi-input, hierarchical, and others) to support randomized functionalities

Simulation-Based Selective Opening Security for Receivers under Chosen-Ciphertext Attacks

Security against selective opening attack (SOA) for receivers requires that in a multi-user setting, even if an adversary has access to all ciphertexts, and adaptively corrupts some fraction of the users to obtain the decryption keys corresponding to some of the ciphertexts, the remaining (potentially related) ciphertexts retain their privacy. In this paper, we study simulation-based selective opening security for receivers of public key encryption (PKE) schemes under chosen-ciphertext attacks (RSIM-SO-CCA). Concretely, we first show that some known PKE schemes meet RSIM-SO-CCA security. Then, we introduce the notion of master-key SOA security for identity-based encryption (IBE), and extend the Canetti-Halevi-Katz (CHK) transformation to show generic PKE constructions achieving RSIM-SO-CCA security. Finally, we show how to construct an IBE scheme achieving master-key SOA security