International Association
for Cryptologic Research

for Dilithium, the post-quantum signature scheme recently standardized by NIST. We improve the masked generation of the masking vector y, based on a fast Booleanto- arithmetic conversion modulo q. We also describe an optimized gadget for the high-order masked rejection sampling, with a complexity independent from the size of the modulus q. We prove the security of our gadgets in the classical ISW t-probing model. Finally, we detail our open-source C implementation of these gadgets integrated into a fully masked Dilithium implementation, and provide an efficiency comparison with previous works.

We present an algorithm solving the ROS ( R andom inhomogeneities in a O verdetermined S olvable system of linear equations) problem mod p in polynomial time for $$\ell > \log p$$ ℓ > log p dimensions. Our algorithm can be combined with Wagner’s attack, and leads to a sub-exponential solution for any dimension $$\ell $$ ℓ with the best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto–Schnorr blind signatures, threshold signatures such as GJKR and the original version of FROST, multisignatures such as CoSI and the two-round version of MuSig, partially blind signatures such as Abe–Okamoto, and conditional blind signatures such as ZGP17. Schemes for e-cash (such as Brands’ signature) and anonymous credentials (such as Anonymous Credentials Light) inspired from the above are also affected.

We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem mod p in polynomial time for $l > log p$ dimensions. Our algorithm can be combined with Wagner's attack, and leads to a sub-exponential solution for any dimension $l$ with best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto--Schnorr blind signatures, threshold signatures such as GJKR and the original version of FROST, multisignatures such as CoSI and the two-round version of MuSig, partially blind signatures such as Abe--Okamoto, and conditional blind signatures such as ZGP17. Schemes for e-cash and anonymous credentials (such as Anonymous Credentials Light) inspired from the above are also affected.

The private join and compute (PJC) functionality enables secure computation over data distributed across different databases, and is applicable to a wide range of applications, many of which address settings where the input databases are of significantly different sizes. We introduce the notion of private information retrieval (PIR) with default, which enables two-party PJC functionalities in a way that hides the size of the intersection of the two databases and incurs sublinear communication cost in the size of the bigger database. We provide two constructions for this functionality, one of which requires offline linear communication, which can be amortized across queries, and one that provides sublinear cost for each query but relies on more computationally expensive tools. We construct inner-product PJC, which has applications to ads conversion measurement and contact tracing, relying on an extension of PIR with default. We evaluate the efficiency of our constructions, which can enable $\mathbf{2^{8}}$ PIR with default lookups on a database of size $\mathbf{2^{25}}$ (or inner-product PJC on databases with such sizes) with the communication of $\mathbf{44}$MB, which costs less than $\mathbf{0.17}$c. for the client and $\mathbf{26.48}$c. for the server.

We present a cryptographic construction for anonymous tokens with private metadata bit, called PMBTokens. This primitive enables an issuer to provide a user with a lightweight, single-use anonymous trust token that can embed a single private bit, which is accessible only to the party who holds the secret authority key and is private with respect to anyone else. Our construction generalizes and extends the functionality of Privacy Pass (PETS’18) with this private metadata bit capability. It provides unforgeability, unlinkability, and privacy for the metadata bit properties based on the DDH and CTDH assumptions in the random oracle model. Both Privacy Pass and PMBTokens rely on non-interactive zero-knowledge proofs (NIZKs). We present new techniques to remove the need for NIZKs, while still achieving unlinkability. We implement our constructions and we report their efficiency costs.

A conjunction is a function $$f(x_1,\dots ,x_n) = \bigwedge _{i \in S} l_i$$ where $$S \subseteq [n]$$ and each $$l_i$$ is $$x_i$$ or $$\lnot x_i$$. Bishop et al. (CRYPTO 2018) recently proposed obfuscating conjunctions by embedding them in the error positions of a noisy Reed-Solomon codeword and placing the codeword in a group exponent. They prove distributional virtual black box (VBB) security in the generic group model for random conjunctions where $$|S| \ge 0.226n$$. While conjunction obfuscation is known from LWE [31, 47], these constructions rely on substantial technical machinery.In this work, we conduct an extensive study of simple conjunction obfuscation techniques. We abstract the Bishop et al. scheme to obtain an equivalent yet more efficient “dual” scheme that can handle conjunctions over exponential size alphabets. This scheme admits a straightforward proof of generic group security, which we combine with a novel combinatorial argument to obtain distributional VBB security for |S| of any size.If we replace the Reed-Solomon code with a random binary linear code, we can prove security from standard LPN and avoid encoding in a group. This addresses an open problem posed by Bishop et al. to prove security of this simple approach in the standard model.We give a new construction that achieves information theoretic distributional VBB security and weak functionality preservation for $$|S| \ge n - n^\delta $$ and $$\delta < 1$$. Assuming discrete log and $$\delta < 1/2$$, we satisfy a stronger notion of functionality preservation for computationally bounded adversaries while still achieving information theoretic security.

We construct public-key function-private predicate encryption for the “small superset functionality,” recently introduced by Beullens and Wee (PKC 2019). This functionality captures several important classes of predicates:Point functions. For point function predicates, our construction is equivalent to public-key function-private anonymous identity-based encryption.Conjunctions. If the predicate computes a conjunction, our construction is a public-key function-private hidden vector encryption scheme. This addresses an open problem posed by Boneh, Raghunathan, and Segev (ASIACRYPT 2013).d-CNFs and read-once conjunctions of d-disjunctions for constant-size d. Our construction extends the group-based obfuscation schemes of Bishop et al. (CRYPTO 2018), Beullens and Wee (PKC 2019), and Bartusek et al. (EUROCRYPT 2019) to the setting of public-key function-private predicate encryption. We achieve an average-case notion of function privacy, which guarantees that a decryption key $$\mathsf {sk} _f$$ reveals nothing about f as long as f is drawn from a distribution with sufficient entropy. We formalize this security notion as a generalization of the (enhanced) real-or-random function privacy definition of Boneh, Raghunathan, and Segev (CRYPTO 2013). Our construction relies on bilinear groups, and we prove security in the generic bilinear group model.

In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes.