## CryptoDB

### Mohammad Hajiabadi

#### Publications

**Year**

**Venue**

**Title**

2021

CRYPTO

Compact Ring Signatures from Learning With Errors
📺
Abstract

Ring signatures allow a user to sign a message on behalf of a ``ring'' of signers, while hiding the true identity of the signer. As the degree of anonymity guaranteed by a ring signature is directly proportional to the size of the ring, an important goal in cryptography is to study constructions that minimize the size of the signature as a function of the number of ring members.
In this work, we present the first compact ring signature scheme (i.e., where the size of the signature grows logarithmically with the size of the ring) from the (plain) learning with errors (LWE) problem. The construction is in the standard model and it does not rely on a trusted setup or on the random oracle heuristic. In contrast with the prior work of Backes
\etal~[EUROCRYPT'2019], our scheme does not rely on bilinear pairings, which allows us to show that the scheme is post-quantum secure assuming the quantum hardness of LWE.
At the heart of our scheme is a new construction of compact and statistically witness-indistinguishable ZAP arguments for NP $\cap$ coNP, that we show to be sound based on the plain LWE assumption. Prior to our work, statistical ZAPs (for all of NP) were known to exist only assuming \emph{sub-exponential} LWE. We believe that this scheme might find further applications in the future.

2020

EUROCRYPT

Two-Round Oblivious Transfer from CDH or LPN
📺
Abstract

We show a new general approach for constructing maliciously-secure two-round oblivious transfer (OT). Specifically, we provide a generic sequence of transformations to upgrade a very basic notion of two-roundOT, which we call elementary OT, to UC-secure OT. We then give simple constructions of elementary OT under the Computational Diffie-Hellman(CDH) assumption or the Learning Parity with Noise (LPN) assumption, yielding the first constructions of malicious (UC-secure) two-round OT under these assumptions. Since two-round OT is complete for two-round 2-party and multi-party computation in the malicious setting, we also achieve the first constructions of the latter under these assumptions.

2020

PKC

Master-Key KDM-Secure IBE from Pairings
📺
Abstract

Identity-based encryption (IBE) is a generalization of public-key encryption (PKE) by allowing encryptions to be made to user identities. In this work, we seek to obtain IBE schemes that achieve key-dependent-message (KDM) security with respect to messages that depend on the master secret key. Previous KDM-secure schemes only achieved KDM security in simpler settings, in which messages may only depend on user secret keys. An important motivation behind studying master-KDM security is the application of this notion in obtaining generic constructions of KDM-CCA secure PKE, a primitive notoriously difficult to realize. We give the first IBE that achieves master-KDM security from standard assumptions in pairing groups. Our construction is modular and combines techniques from KDM-secure PKE based from hash-proof systems, together with IBE that admits a tight security proof in the multi-challenge setting, which happens to be unexpectedly relevant in the context of KDM security. In fact, to the best of our knowledge, this is the first setting where techniques developed in the context of realizing tightly secure cryptosystems have led to a new feasibility result. As a byproduct, our KDM-secure IBE, and thus the resulting KDM-CCA-secure PKE both enjoy a tight security reduction, independent of the number of challenge ciphertexts, which was not achieved before.

2020

TCC

Efficient Range-Trapdoor Functions and Applications: Rate-1 OT and More
Abstract

Substantial work on trapdoor functions (TDFs) has led to many powerful notions
and applications. However, despite tremendous work and progress, all known
constructions have prohibitively large public keys.
In this work, we introduce new techniques for realizing so-called range-trapdoor hash functions with short public keys. This notion, introduced by Döttling et al. [Crypto 2019], allows for encoding a range of indices into a public key in a way that the public key leaks no information about the range, yet an associated trapdoor enables recovery of the corresponding input part.
We give constructions of range-trapdoor hash functions, where for a given range $I$ the public key consists of $O(n)$ group elements, improving upon $O(n |I|)$ achieved by Döttling et al. Moreover, by designing our evaluation algorithm in a special way involving Toeplitz matrix multiplication and by showing how to perform fast-Fourier transforms in the exponent, we arrive at $O(n \log n)$ group operations for evaluation, improving upon $O(n^2)$, required of previous constructions. Our constructions rely on power-DDH assumptions in pairing-free groups.
As applications of our results we obtain
--- The first construction of (rate-1) lossy TDFs with public keys consisting of a linear number of group elements (without pairings).
--- Rate-1 string OT with receiver communication complexity of $O(n)$ group elements, where $n$ is the sender's message size, improving upon $O(n^2)$ [Crypto 2019]. This leads to a similar result in the context of private-information retrieval (PIR).
--- Semi-compact homomorphic encryption for branching programs: A construction of homomorphic encryption for branching programs, with ciphertexts consisting of $O(\lambda n d)$ group elements, improving upon $O(\lambda^2 n d)$. Here $\lambda $ denotes the security parameter, $n$ the input size and $d$ the depth of the program.

2019

PKC

Registration-Based Encryption from Standard Assumptions
Abstract

The notion of Registration-Based Encryption (RBE) was recently introduced by Garg, Hajiabadi, Mahmoody, and Rahimi [TCC’18] with the goal of removing the private-key generator (PKG) from IBE. Specifically, RBE allows encrypting to identities using a (compact) master public key, like how IBE is used, with the benefit that the PKG is substituted with a weaker entity called “key curator” who has no knowledge of any secret keys. Here individuals generate their secret keys on their own and then publicly register their identities and their corresponding public keys to the key curator. Finally, individuals obtain “rare” decryption-key updates from the key curator as the population grows. In their work, they gave a construction of RBE schemes based on the combination of indistinguishability obfuscation and somewhere statistically binding hash functions. However, they left open the problem of constructing RBE schemes based on standard assumptions.In this work, we resolve the above problem and construct RBE schemes based on standard assumptions (e.g., CDH or LWE). Furthermore, we show a new application of RBE in a novel context. In particular, we show that anonymous variants of RBE (which we also construct under standard assumptions) can be used for realizing abstracts forms of anonymous messaging tasks in simple scenarios in which the parties communicate by writing messages on a shared board in a synchronized way.

2019

EUROCRYPT

New Techniques for Efficient Trapdoor Functions and Applications
📺
Abstract

We develop techniques for constructing trapdoor functions (TDFs) with short image size and advanced security properties. Our approach builds on the recent framework of Garg and Hajiabadi [CRYPTO 2018]. As applications of our techniques, we obtainThe first construction of deterministic-encryption schemes for block-source inputs (both for the CPA and CCA cases) based on the Computational Diffie-Hellman (CDH) assumption. Moreover, by applying our efficiency-enhancing techniques, we obtain CDH-based schemes with ciphertext size linear in plaintext size.The first construction of lossy TDFs based on the Decisional Diffie-Hellman (DDH) assumption with image size linear in input size, while retaining the lossiness rate of [Peikert-Waters STOC 2008].
Prior to our work, all constructions of deterministic encryption based even on the stronger DDH assumption incurred a quadratic gap between the ciphertext and plaintext sizes. Moreover, all DDH-based constructions of lossy TDFs had image size quadratic in the input size.At a high level, we break the previous quadratic barriers by introducing a novel technique for encoding input bits via hardcore output bits with the use of erasure-resilient codes. All previous schemes used group elements for encoding input bits, resulting in quadratic expansions.

2019

ASIACRYPT

Rate-1 Trapdoor Functions from the Diffie-Hellman Problem
Abstract

Trapdoor functions (TDFs) are one of the fundamental building blocks in cryptography. Studying the underlying assumptions and the efficiency of the resulting instantiations is therefore of both theoretical and practical interest. In this work we improve the input-to-image rate of TDFs based on the Diffie-Hellman problem. Specifically, we present: (a)A rate-1 TDF from the computational Diffie-Hellman (CDH) assumption, improving the result of Garg, Gay, and Hajiabadi [EUROCRYPT 2019], which achieved linear-size outputs but with large constants. Our techniques combine non-binary alphabets and high-rate error-correcting codes over large fields.(b)A rate-1 deterministic public-key encryption satisfying block-source security from the decisional Diffie-Hellman (DDH) assumption. While this question was recently settled by Döttling et al. [CRYPTO 2019], our scheme is conceptually simpler and concretely more efficient. We demonstrate this fact by implementing our construction.

2018

CRYPTO

Limits on the Power of Garbling Techniques for Public-Key Encryption
📺
Abstract

Understanding whether public-key encryption can be based on one-way functions is a fundamental open problem in cryptography. The seminal work of Impagliazzo and Rudich [STOC’89] shows that black-box constructions of public-key encryption from one-way functions are impossible. However, this impossibility result leaves open the possibility of using non-black-box techniques for achieving this goal.One of the most powerful classes of non-black-box techniques, which can be based on one-way functions (OWFs) alone, is Yao’s garbled circuit technique [FOCS’86]. As for the non-black-box power of this technique, the recent work of Döttling and Garg [CRYPTO’17] shows that the use of garbling allows us to circumvent known black-box barriers in the context of identity-based encryption.We prove that garbling of circuits that have OWF (or even random oracle) gates in them are insufficient for obtaining public-key encryption. Additionally, we show that this model also captures (non-interactive) zero-knowledge proofs for relations with OWF gates. This indicates that currently known OWF-based non-black-box techniques are perhaps insufficient for realizing public-key encryption.

2018

CRYPTO

Trapdoor Functions from the Computational Diffie-Hellman Assumption
📺
Abstract

Trapdoor functions (TDFs) are a fundamental primitive in cryptography. Yet, the current set of assumptions known to imply TDFs is surprisingly limited, when compared to public-key encryption. We present a new general approach for constructing TDFs. Specifically, we give a generic construction of TDFs from any Chameleon Encryption (Döttling and Garg [CRYPTO’17]) satisfying a novel property which we call recyclability. By showing how to adapt current Computational Diffie-Hellman (CDH) based constructions of chameleon encryption to yield recyclability, we obtain the first construction of TDFs with security proved under the CDH assumption. While TDFs from the Decisional Diffie-Hellman (DDH) assumption were previously known, the possibility of basing them on CDH had remained open for more than 30 years.

2018

PKC

New Constructions of Identity-Based and Key-Dependent Message Secure Encryption Schemes
Abstract

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 KDM-secure secret-key encryption scheme and any public-key encryption scheme.

2018

TCC

Enhancements are Blackbox Non-trivial: Impossibility of Enhanced Trapdoor Permutations from Standard Trapdoor Permutations
Abstract

Trapdoor permutations (TDP) are a fundamental primitive in cryptography. Several variants of this notion have emerged as a result of different applications. However, it is not clear whether these variants can be based on the standard notion of TDPs.We study the question of whether enhanced trapdoor permutations can be based on classical trapdoor permutations. The main motivation of our work is in the context of existing TDP-based constructions of oblivious transfer and non-interactive zero knowledge protocols, which require enhancements to the classical TDP notion. We prove that these enhancements are non-trivial, in the sense that there does not exist fully blackbox constructions of enhanced TDPs from classical TDPs.On the technical side, we show that the enhanced TDP security of any construction in the random TDP oracle world can be broken via a polynomial number of queries to the TDP oracle as well as a weakening oracle, which provides inversion with respect to randomness. We also show that the standard one-wayness of the random TDP oracle stays intact in the presence of this weakening oracle.

2018

TCC

Registration-Based Encryption: Removing Private-Key Generator from IBE
Abstract

In this work, we introduce the notion of registration-based encryption (RBE for short) with the goal of removing the trust parties need to place in the private-key generator in an IBE scheme. In an RBE scheme, users sample their own public and secret keys. There will also be a “key curator” whose job is only to aggregate the public keys of all the registered users and update the “short” public parameter whenever a new user joins the system. Encryption can still be performed to a particular recipient using the recipient’s identity and any public parameters released subsequent to the recipient’s registration. Decryption requires some auxiliary information connecting users’ public (and secret) keys to the public parameters. Because of this, as the public parameters get updated, a decryptor may need to obtain “a few” additional auxiliary information for decryption. More formally, if n is the total number of identities and $$\mathrm {\kappa }$$κ is the security parameter, we require the following.Efficiency requirements: (1) A decryptor only needs to obtain updated auxiliary information for decryption at most $$O(\log n)$$O(logn) times in its lifetime, (2) each of these updates are computed by the key curator in time $${\text {poly}}(\mathrm {\kappa },\log n)$$poly(κ,logn), and (3) the key curator updates the public parameter upon the registration of a new party in time $${\text {poly}}(\mathrm {\kappa },\log n)$$poly(κ,logn). Properties (2) and (3) require the key curator to have random access to its data.Compactness requirements: (1) Public parameters are always at most $${\text {poly}}(\mathrm {\kappa },\log n)$$poly(κ,logn) bit, and (2) the total size of updates a user ever needs for decryption is also at most $${\text {poly}}(\mathrm {\kappa },\log n)$$poly(κ,logn) bits.We present feasibility results for constructions of RBE based on indistinguishably obfuscation. We further provide constructions of weakly efficient RBE, in which the registration step is done in $${\text {poly}}(\mathrm {\kappa },n)$$poly(κ,n), based on CDH, Factoring or LWE assumptions. Note that registration is done only once per identity, and the more frequent operation of generating updates for a user, which can happen more times, still runs in time $${\text {poly}}(\mathrm {\kappa },\log n)$$poly(κ,logn). We leave open the problem of obtaining standard RBE (with $${\text {poly}}(\mathrm {\kappa },\log n)$$poly(κ,logn) registration time) from standard assumptions.

2017

EUROCRYPT

2016

PKC

2015

EPRINT

#### Program Committees

- Eurocrypt 2020
- TCC 2020

#### Coauthors

- Jonathan Bootle (1)
- Andrea Cerulli (1)
- Rahul Chatterjee (1)
- Nico Döttling (3)
- Sanjam Garg (11)
- Romain Gay (2)
- Essam Ghadafi (1)
- Jens Groth (1)
- Sune K. Jakobsen (1)
- Bruce M. Kapron (8)
- Dakshita Khurana (1)
- Xiaohui Liang (1)
- Kevin Liu (1)
- Mohammad Mahmoody (3)
- Giulio Malavolta (2)
- Daniel Masny (2)
- Ameer Mohammed (1)
- Rafail Ostrovsky (1)
- Omkant Pandey (1)
- Ahmadreza Rahimi (2)
- Sruthi Sekar (1)
- Sina Shiehian (1)
- Venkatesh Srinivasan (2)
- Daniel Wichs (1)