We present a somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security (quantumly) reduces to the worst-case hardness of problems on ideal lattices. We then transform it into a fully homomorphic encryption scheme using standard "squashing" and "bootstrapping" techniques introduced by Gentry (STOC 2009).

One of the obstacles in going from "somewhat" to full homomorphism is the requirement that the somewhat homomorphic scheme be circular secure, namely, the scheme can be used to securely encrypt its own secret key. For all known somewhat homomorphic encryption schemes, this requirement was not known to be achievable under any cryptographic assumption, and had to be explicitly assumed. We take a step forward towards removing this additional assumption by proving that our scheme is in fact secure when encrypting polynomial functions of the secret key.

Our scheme is based on the ring learning with errors (RLWE) assumption that was recently introduced by Lyubashevsky, Peikert and Regev (Eurocrypt 2010). The RLWE assumption is reducible to worstcase problems on ideal lattices, and allows us to completely abstract out the lattice interpretation, resulting in an extremely simple scheme. For example, our secret key is s, and our public key is (a, b = as+2e), where s, a, e are all degree (n - 1) integer polynomials whose coefficients are independently drawn from easy to sample distributions.

/pdf/fully-homomorphic-encryption-from-ring-lwe-and-security-for-2wxkyjv9e4.pdf

Fully homomorphic encryption from ring-LWE and security for key dependent messages

The best lattice reduction algorithm known in practice for high dimension is Schnorr-Euchner's BKZ: all security estimates of lattice cryptosystems are based on NTL's old implementation of BKZ. However, recent progress on lattice enumeration suggests that BKZ and its NTL implementation are no longer optimal, but the precise impact on security estimates was unclear. We assess this impact thanks to extensive experiments with BKZ 2.0, the first state-of-the-art implementation of BKZ incorporating recent improvements, such as Gama-Nguyen-Regev pruning. We propose an efficient simulation algorithm to model the behaviour of BKZ in high dimension with high blocksize ≥50, which can predict approximately both the output quality and the running time, thereby revising lattice security estimates. For instance, our simulation suggests that the smallest NTRUSign parameter set, which was claimed to provide at least 93-bit security against key-recovery lattice attacks, actually offers at most 65-bit security.

/pdf/bkz-2-0-better-lattice-security-estimates-1i0txm8k41.pdf

BKZ 2.0: better lattice security estimates

NTRUEncrypt, proposed in 1996 by Hoffstein, Pipher and Silverman, is the fastest known lattice-based encryption scheme. Its moderate key-sizes, excellent asymptotic performance and conjectured resistance to quantum computers could make it a desirable alternative to factorisation and discrete-log based encryption schemes. However, since its introduction, doubts have regularly arisen on its security. In the present work, we show how to modify NTRUEncrypt to make it provably secure in the standard model, under the assumed quantum hardness of standard worst-case lattice problems, restricted to a family of lattices related to some cyclotomic fields. Our main contribution is to show that if the secret key polynomials are selected by rejection from discrete Gaussians, then the public key, which is their ratio, is statistically indistinguishable from uniform over its domain. The security then follows from the already proven hardness of the R-LWE problem.

/pdf/making-ntru-as-secure-as-worst-case-problems-over-ideal-1duiiskfq4.pdf

Making NTRU as secure as worst-case problems over ideal lattices

Attribute-based encryption (ABE), as introduced by Sahai and Waters, allows for fine-grained access control on encrypted data. In its key-policy flavor, the primitive enables senders to encrypt messages under a set of attributes and private keys are associated with access structures that specify which ciphertexts the key holder will be allowed to decrypt. In most ABE systems, the ciphertext size grows linearly with the number of ciphertext attributes and the only known exceptions only support restricted forms of threshold access policies.

This paper proposes the first key-policy attribute-based encryption (KP-ABE) schemes allowing for non-monotonic access structures (i.e., that may contain negated attributes) and with constant ciphertext size. Towards achieving this goal, we first show that a certain class of identity-based broadcast encryption schemes generically yields monotonic KPABE systems in the selective set model. We then describe a new efficient identity-based revocation mechanism that, when combined with a particular instantiation of our general monotonic construction, gives rise to the first truly expressive KP-ABE realization with constant-size ciphertexts. The downside of these new constructions is that private keys have quadratic size in the number of attributes. On the other hand, they reduce the number of pairing evaluations to a constant, which appears to be a unique feature among expressive KP-ABE schemes.

/pdf/expressive-key-policy-attribute-based-encryption-with-4qn1djik63.pdf

Expressive key-policy attribute-based encryption with constant-size ciphertexts

Masking is a well-known countermeasure to protect block cipher implementations against side-channel attacks The principle is to randomly split every sensitive intermediate variable occurring in the computation into d + 1 shares, where d is called the masking order and plays the role of a security parameter Although widely used in practice, masking is often considered as an empirical solution and its effectiveness is rarely proved In this paper, we provide a formal security proof for masked implementations of block ciphers Specifically, we prove that the information gained by observing the leakage from one execution can be made negligible (in the masking order) To obtain this bound, we assume that every elementary calculation in the implementation leaks a noisy function of its input, where the amount of noise can be chosen by the designer (yet linearly bounded) We further assume the existence of a leak-free component that can refresh the masks of shared variables Our work can be viewed as an extension of the seminal work of Chari et alpublished at CRYPTO in 1999 on the soundness of combining masking with noise to thwart side-channel attacks

/pdf/masking-against-side-channel-attacks-a-formal-security-proof-gq2py69z3w.pdf

Masking against Side-Channel Attacks: A Formal Security Proof

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

Henri Gilbert

Papers

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