Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS – Cryptographic Suite for Algebraic Lattices – a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki–Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security.

/pdf/crystals-kyber-a-cca-secure-module-lattice-based-kem-1bkiyrcfqr.pdf

CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM

Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems. Attractive features of lattice cryptography include apparent resistance to quantum attacks (in contrast with most number-theoretic cryptography), high asymptotic efficiency and parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. This work surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems (and their more efficient ring-based variants), their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

/pdf/a-decade-of-lattice-cryptography-47cz03fxsi.pdf

A Decade of Lattice Cryptography.

Cryptosystems I.- On Ideal Lattices and Learning with Errors over Rings.- Fully Homomorphic Encryption over the Integers.- Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups.- Fully Secure Functional Encryption: Attribute-Based Encryption and (Hierarchical) Inner Product Encryption.- Obfuscation and Side Channel Security.- Secure Obfuscation for Encrypted Signatures.- Public-Key Encryption in the Bounded-Retrieval Model.- Protecting Circuits from Leakage: the Computationally-Bounded and Noisy Cases.- 2-Party Protocols.- Partial Fairness in Secure Two-Party Computation.- Secure Message Transmission with Small Public Discussion.- On the Impossibility of Three-Move Blind Signature Schemes.- Efficient Device-Independent Quantum Key Distribution.- Cryptanalysis.- New Generic Algorithms for Hard Knapsacks.- Lattice Enumeration Using Extreme Pruning.- Algebraic Cryptanalysis of McEliece Variants with Compact Keys.- Key Recovery Attacks of Practical Complexity on AES-256 Variants with up to 10 Rounds.- IACR Distinguished Lecture.- Cryptography between Wonderland and Underland.- Automated Tools and Formal Methods.- Automatic Search for Related-Key Differential Characteristics in Byte-Oriented Block Ciphers: Application to AES, Camellia, Khazad and Others.- Plaintext-Dependent Decryption: A Formal Security Treatment of SSH-CTR.- Computational Soundness, Co-induction, and Encryption Cycles.- Models and Proofs.- Encryption Schemes Secure against Chosen-Ciphertext Selective Opening Attacks.- Cryptographic Agility and Its Relation to Circular Encryption.- Bounded Key-Dependent Message Security.- Multiparty Protocols.- Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography.- Adaptively Secure Broadcast.- Universally Composable Quantum Multi-party Computation.- Cryptosystems II.- A Simple BGN-Type Cryptosystem from LWE.- Bonsai Trees, or How to Delegate a Lattice Basis.- Efficient Lattice (H)IBE in the Standard Model.- Hash and MAC.- Multi-property-preserving Domain Extension Using Polynomial-Based Modes of Operation.- Stam's Collision Resistance Conjecture.- Universal One-Way Hash Functions via Inaccessible Entropy.- Foundational Primitives.- Constant-Round Non-malleable Commitments from Sub-exponential One-Way Functions.- Constructing Verifiable Random Functions with Large Input Spaces.- Adaptive Trapdoor Functions and Chosen-Ciphertext Security.

Advances in cryptology -- EUROCRYPT 2010 : 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, May 30-June 3, 2010 : proceedings

We explore cryptographic primitives with low multiplicative complexity. This is motivated by recent progress in practical applications of secure multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge proofs (ZK) where primitives from symmetric cryptography are needed and where linear computations are, compared to non-linear operations, essentially “free”. Starting with the cipher design strategy “LowMC” from Eurocrypt 2015, a number of bit-oriented proposals have been put forward, focusing on applications where the multiplicative depth of the circuit describing the cipher is the most important optimization goal.

/pdf/mimc-efficient-encryption-and-cryptographic-hashing-with-2r5zm2q9yj.pdf

MiMC: Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity

Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems. Attractive features of lattice cryptography include apparent resistance to quantum attacks in contrast with most number-theoretic cryptography, high asymptotic efficiency and parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. This work surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution SIS and learning with errors LWE problems and their more efficient ring-based variants, their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

/pdf/a-decade-of-lattice-cryptography-4em28paukr.pdf

A Decade of Lattice Cryptography

SPRING is a family of pseudo-random functions that aims to combine the guarantees of security reductions with good performance on a variety of platforms. Preliminary software implementations for small-parameter instantiations of SPRING were proposed at FSE 2014, and have been demonstrated to reach throughputs within small factors of those of AES. In this paper, we complement these results and investigate the hardware design space of these types of primitives.

Our first pragmatic contribution is the first FPGA implementation of SPRING in a counter-like mode. We show that the "rounded product" operations in our design can be computed efficiently, reaching throughputs in the hundreds of megabits/second range within only 4% of the resources of a modern Xilinx Virtex-6 reconfigurable device. Our second more prospective contribution is to discuss the properties of SPRING hardware implementations for side-channel resistance. We show that a part of the design can be very efficiently masked with linear overhead, while another part implies quadratic overhead due to non-linear operations similarly to what is usually observed, e.g., for block ciphers. Yet, we argue that for this second part of the design, resistance against "simple power analysis" may be sufficient to obtain concrete implementation security. We suggest ways to reach this goal very efficiently, via shuffling. We believe that such hybrid implementations, where each part of the design is protected with adequate solutions, is a promising topic for further investigation.

/pdf/fpga-implementations-of-spring-5bxjom7p24.pdf

FPGA Implementations of SPRING

Recently, Banerjee, Peikert and Rosen (EUROCRYPT 2012) proposed new theoretical pseudorandom function candidates based on “rounded products” in certain polynomial rings, which have rigorously provable security based on worst-case lattice problems. The functions also enjoy algebraic properties that make them highly parallelizable and attractive for modern applications, such as evaluation under homomorphic encryption schemes. However, the parameters required by BPR’s security proofs are too large for practical use, and many other practical aspects of the design were left unexplored in that work.

/pdf/spring-fast-pseudorandom-functions-from-rounded-ring-1xovhbidjk.pdf

SPRING: Fast Pseudorandom Functions from Rounded Ring Products

The notion of non-malleability in cryptography refers to the setting where the adversary is a man-in-the-middle (MIM) who takes part in two or more protocol executions and tries to use information obtained in one, to violate the security of another. Despite two decades of research, non-malleable commitments (NMCs) have remained too inefficient to be implemented in practice, without some sort of trusted setup. In this work, we give a fast implementation of NMC in the plain model, based on the DDH assumption being hard over elliptic curve groups. Our main theoretical result is a new NMC scheme which can be thought of as a "high dimensional" generalization of the one in the recent work of [GRRV14]. Central to our efficiency improvements is a method of constraining challenges sent by the receiver. This new approach enables us to obtain dramatically improved parameters over those suggested in [GRRV14]. In particular, our work opens the door to implementations based on Elliptic Curves. Our prototype implementation gives evidence of our protocol's efficiency. Additionally, like the Elgamal commitment it is built on top of, our scheme allows for homomrphic operations on committed values, and is amenable to fast Schnorr proofs of knowledge. Thus, it will work well when used as a building block inside larger cryptographic protocols. As an example of its performance, our protocol allows a committer to commit to a 1.9-KB message using a scheme supporting 220 identities in less than one second.

Fast Non-Malleable Commitments

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FPGA Implementations of SPRING

SPRING: Fast Pseudorandom Functions from Rounded Ring Products

Fast Non-Malleable Commitments