Generalized public-key cryptography with tight security

Book Chapter, Contemporary Topics in Mathematics and Statistics with Applications, Volume-I, Asian Books Pvt Ltd., 2012

From its inception, public-key cryptosystems have been an area of active research. Various aspects of public-key encryption like constructions, security notions, adversarial models, hardness assumptions, proof-methodology, efficiency, compatibility etc. have been analysed and re-analysed in the last three and half decades by numerous cryptographers. Some of them are good enough to survive while some of them, though broken, provides meaningful insights towards the subject. In this article, our aim is to provide an expository as well as technical (as far as possible, keeping in mind its brevity) overview of the subject as it has progressed over the years, along with some open problems and suitable references.

IACR Cryptol. ePrint Arch., 2018

In this paper, we introduce a new framework for constructing public-key encryption (PKE) schemes resilient to joint post-challenge/after-the-fact leakage and tampering attacks in the bounded leakage and tampering (BLT) model, introduced by Damgard et al. (Asiacrypt 2013). All the prior formulations of PKE schemes considered leakage and tampering attacks only before the challenge ciphertext is made available to the adversary. However, this restriction seems necessary, since achieving security against post-challenge leakage and tampering attacks in its full generality is impossible, as shown in previous works. In this paper, we study the post-challenge/after-the-fact security for PKE schemes against bounded leakage and tampering under a restricted yet meaningful and reasonable notion of security, namely, the split-state leakage and tampering model. We show that it is possible to construct secure PKE schemes in this model, tolerating arbitrary (but bounded) leakage and tampering querie...

Information Processing Letters, 2008

In public key encryption schemes with a double decryption mechanism (DD-PKE), decryption can be done in either of two ways: by the user owning the secret/public key pair corresponding to the ciphertext, or by a trusted party holding a sort of master secret-key. In this note we argue that the classical security notion for standard public key encryption schemes does not suffice for DD-PKE schemes, and propose a new natural definition. Additionally, we illustrate the usefulness of the new security definition by showing that a DD-PKE scheme presented in the workshop Selected Areas in Cryptography 2005 is insecure under this augmented security notion.

Public-Key Cryptography – PKC 2016, 2016

We propose generic constructions of public-key encryption schemes, satisfying key-dependent message (KDM) security for projections and different forms of key-leakage resilience, from CPA-secure private-key encryption schemes with two main abstract properties: (1) a form of (additive) homomorphism with respect to both plaintexts and randomness, and (2) reproducibility, providing a means for reusing encryption randomness across independent secret keys. More precisely, our construction transforms a private-key scheme with the stated properties (and one more mild condition) into a public-key one, providing:

Lecture Notes in Computer Science, 1999

This paper proposes two new public-key cryptosystems semantically secure against adaptive chosen-ciphertext attacks. Inspired from a recently discovered trapdoor technique based on composite-degree residues, our converted encryption schemes are proven, in the random oracle model, secure against active adversaries (NM-CCA2) under the assumptions that the Decision Composite Residuosity and Decision Partial Discrete Logarithms problems are intractable. We make use of specific techniques that differ from Bellare-Rogaway or Fujisaki-Okamoto conversion methods. Our second scheme is specifically designed to be efficient for decryption and could provide an elegant alternative to OAEP.

Lecture Notes in Computer Science, 2003

At Crypto'99, Fujisaki and Okamoto [8] presented a nice generic transformation from weak asymmetric and symmetric schemes into an IND-CCA hybrid encryption scheme in the Random Oracle Model. Two specific candidates for standardization were designed from this transformation: PSEC-2 [14] and EPOC-2 [7], based on El Gamal and Okamoto-Uchiyama primitives, respectively. Since then, several cryptanalysis of EPOC have been published, one in the Chosen Ciphertext Attack game, and others making use of a poor implementation that is vulnerable to reject timing attacks. The aim of this work is to prevent such attacks from generic transformation by identifying the properties that an asymmetric scheme must have in order to obtain a secure hybrid scheme. To achieve this, some ambiguities in the proof of the generic transformation [8] which could lead to false claims are described. As a result, the original conversion is modified and the class of asymmetric primitives that can be used is shortened. Secondly, the concept of Easy Verifiable Primitive is formalized, showing its connection with Gap problems. Using these ideas, a new security proof for the modified transformation is given. The good news is that the reduction is tight, improving the concrete security claimed in the original work for the Easy Verifiable Primitives. For the rest of primitives, the concrete security is improved at the cost of stronger assumptions. Finally, the new conversion's resistance to reject timing attacks is addressed.

This paper presents a weakness in the key schedule of the AES candidate HPC (Hasty Pudding Cipher). It is shown that for the HPC version with a 128-bit key, 1 in 256 keys is weak in the sense that it has 2 30 equivalent keys. An efficient algorithm is proposed to construct these weak keys and the corresponding equivalent keys. If a weak key is used, it can be recovered by exhaustive search trying only 2 89 keys on average. This is an improvement by a factor of 2 38 over a normal exhaustive key search, which requires on average 2 127 attempts. The weakness also implies that HPC cannot be used in standard constructions for hash functions based on block ciphers. The analysis is extended to HPC with a 192-bit key and a 256-bit key, with similar results. For some other key lengths, all keys are shown to be weak. An example of this is the HPC variant with a 56-bit user key and block length of 128 bits, which can be broken in 2 31 attempts on average.

Journal of Mathematical Cryptology

We present a new approach to construct several leakage-resilient cryptographic primitives, including leakage-resilient public-key encryption (PKE) schemes, authenticated key exchange (AKE) protocols and low-latency key exchange (LLKE) protocols. To this end, we introduce a new primitive called leakage-resilient non-interactive key exchange (LR-NIKE) protocol. We introduce an appropriate security model for LR-NIKE protocols in the bounded memory leakage (BML) settings. We then show a secure construction of the LR-NIKE protocol in the BML setting that achieves an optimal leakage rate, i.e., {1-o(1)} . Our construction of LR-NIKE requires a minimal use of a leak-free hardware component. We argue that the use of such a leak-free hardware component seems to be unavoidable in any construction of an LR-NIKE protocol, even in the BML setting. Finally, we show how to construct the aforementioned leakage-resilient primitives from such an LR-NIKE protocol as summarized below. All these primiti...

Viele haben auf die eine oder andere Weise dazu beigetragen, dass diese Dissertation so entstehen konnte, wie sie nun vorliegt. Der Versuch einer vollständigen Aufzählung müsste scheitern; hier seien zunächst die erwähnt, die nicht mit Namen genannt werden können, weil sie als anonyme Gutachter für Konferenzen tätig waren und dabei Anregungen zur Darstellung einiger der hier präsentierten Ergebnisse beigetragen haben. Außerdem zu nennen ist David Hopwood, der in einer früheren Fassung der Ausführungen zur beweisbaren Sicherheit des Mix-Verfahrens (hier in Abschnitt 4.2) eine Lücke aufgespürt hat. Prof. Johannes Buchmann hat es auf bemerkenswerte Weise verstanden, die Arbeitsbedingungen zu schaffen, in denen diese Dissertation gedeihen konnte, und hat wertvolle Anregungen geliefert. Auch alle anderen am Fachgebiet Theoretische Informatik hatten teil daran, eine angenehme und fruchtbare Arbeitsatmosphäre zu schaffen. Danke!

Lecture Notes in Computer Science, 1998

This paper proposes a novel public-key cryptosystem, which is practical, provably secure and has some other interesting properties as follows: 1. Its trapdoor technique is essentially different from any other previous schemes including RSA-Rabin and Diffie-Hellman. 2. It is a probabilistic encryption scheme. 3. It can be proven to be as secure as the intractability of factoring n = p2q (in the sense of the security of the whole plaintext) against passive adversaries. 4. It is semantically secure under the p-subgroup assumption, which is comparable to the quadratic residue and higher degree residue assumptions. 5. Under the most practical environment, the encryption and decryption speeds of our scheme are comparable to (around twice slower than) those of elliptic curve cryptosystems. 6. It has a homomorphic property: E(mo, r0)E(ml, rl) mod n = E(mo+ ml, r2), where E(m, r) means a ciphertext of plaintext m as randomized by r and m0 § ml < p. 7. Anyone can change a ciphertext, C-E(m,r), into another ciphertext, C ~ = Ch "1 mod n, while preserving plaintext of C (i.e.,

Progress in Cryptology …, 2010

Public-key encryption schemes with non-interactive opening (PKENO) allow a receiver to non-interactively convince third parties that a ciphertext decrypts to a given plaintext or, alternatively, that such a ciphertext is invalid. Two practical generic constructions for PKENO have been proposed so far, starting from either identity-based encryption or public-key encryption with witness-recovering decryption (PKEWR). We show that the known transformation from PKEWR to PKENO fails to provide chosen-ciphertext security; only the transformation from identity-based encryption remains thus valid. Next, we prove that PKENO can alternatively be built out of robust non-interactive threshold public-key cryptosystems, a primitive that differs from identitybased encryption. Using the new transformation, we construct two efficient PKENO schemes: one based on the Decisional Diffie-Hellman assumption (in the Random-Oracle Model) and one based on the Decisional Linear assumption (in the standard model). Last but not least, we propose new applications of PKENO in protocol design. Motivated by these applications, we reconsider proof soundness for PKENO and put forward new definitions that are stronger than those considered so far. We give a taxonomy of all definitions and demonstrate them to be satisfiable.

2002

Cryptographic computations (decryption, signature generation, etc.) are often performed on a relatively insecure device (e.g., a mobile device or an Internet-connected host) which cannot be trusted to maintain secrecy of the private key. We propose and investigate the notion of key-insulated security whose goal is to minimize the damage caused by secret-key exposures. In our model, the secret key(s) stored on the insecure device are refreshed at discrete time periods via inter-action with a physically-secure - but computationally-limited - device which stores a “master key”. All cryptographic computations are still done on the insecure device, and the public key remains unchanged. In a (t, N)-key-insulated scheme, an adversary who compromises the insecure device and obtains secret keys for up to t periods of his choice is unable to violate the security of the cryptosystem for any of the remaining N - t periods. Furthermore, the scheme remains secure (for all time periods) against an adversary who compromises only the physically-secure device. We focus primarily on key-insulated public-key encryption. We construct a (t, N)-key-insulated encryption scheme based on any (standard) public-key encryption scheme, and give a more efficient construction based on the DDH assumption. The latter construction is then extended to achieve chosen-ciphertext security.

2006

Token-controlled public key encryption (TCPKE) schemes, introduced in [1], offer many possibilities of application in financial or legal scenarios. Roughly speaking, in a TCPKE scheme messages are encrypted by using a public key together with a secret token, in such a way that the receiver is not able to decrypt this ciphertext until the token is published or released. The communication overhead for releasing the token is small in comparison with the ciphertext size. However, the fact that the same ciphertext could decrypt to different messages under different tokens was not addressed in the original work. In our opinion this is an essential security property that limits the use of this primitive in practice. In this work, we formalize this natural security goal and show that the schemes in [1]are insecure under this notion. In the second place, we propose a very simple and efficient generic construction of TCPKE schemes, starting from any trapdoor partial one-way function. This construction is obtained from a slight but powerful modification of the celebrated Fujisaki-Okamoto transformation [7]. We prove that the resulting schemes satisfy all the required security properties, in the random oracle model. Previous to this work, only particular instantiations of TCPKE schemes were proposed.

Public-Key Cryptography – PKC 2018, 2018

Recently, Döttling and Garg (CRYPTO 2017) showed how to build identity-based encryption (IBE) from a novel primitive termed Chameleon Encryption, which can in turn be realized from simple number theoretic hardness assumptions such as the computational Diffie-Hellman assumption (in groups without pairings) or the factoring assumption. In a follow-up work (TCC 2017), the same authors showed that IBE can also be constructed from a slightly weaker primitive called One-Time Signatures with Encryption (OTSE). In this work, we show that OTSE can be instantiated from hard learning problems such as the Learning With Errors (LWE) and the Learning Parity with Noise (LPN) problems. This immediately yields the first IBE construction from the LPN problem and a construction based on a weaker LWE assumption compared to previous works. Finally, we show that the notion of one-time signatures with encryption is also useful for the construction of key-dependent-message (KDM) secure public-key encryption. In particular, our results imply that a KDM-secure public key encryption can be constructed from any KDMsecure secret-key encryption scheme and any public-key encryption scheme.

2009

Recently, at Crypto 2008, Boneh, Halevi, Hamburg, and Ostrovsky (BHHO) solved the long-standing open problem of “circular encryption,” by presenting a public key encryption scheme and proving that it is semantically secure against key dependent chosen plaintext attack (KDM-CPA security) under standard assumptions (and without resorting to random oracles). However, they left as an open problem that of designing an encryption scheme that simultaneously provides security against both key dependent chosen plaintext and adaptive chosen ciphertext attack (KDM-CCA2 security). In this paper, we solve this problem. First, we show that by applying the Naor-Yung “double encryption” paradigm, one can combine any KDM-CPA secure scheme with any (ordinary) CCA2 secure scheme, along with an appropriate non-interactive zero-knowledge proof, to obtain a KDM-CCA2 secure scheme. Second, we give a concrete instantiation that makes use the above KDM-CPA secure scheme of BHHO, along with a generalization of the Cramer-Shoup CCA2 secure encryption scheme, and recently developed pairing-based NIZK proof systems. This instantiation increases the complexity of the BHHO scheme by just a small constant factor.