National Institute of Standards and Technology における超伝導研究及び生活

An important open problem in the area of Traitor Tracing is designing a scheme with constant expansion of the size of keys (users' keys and the encryption key) and of the size of ciphertexts with respect to the size of the plaintext. This problem is known from the introduction of Traitor Tracing by Chor, Fiat and Naor. We refer to such schemes as traitor tracing with constant transmission rate. Here we present a general methodology and two protocol constructions that result in the first two public-key traitor tracing schemes with constant transmission rate in settings where plaintexts can be calibrated to be sufficiently large. Our starting point is the notion of copyrighted function which was presented by Naccache, Shamir and Stern. We first solve the open problem of discrete-log-based and public-key-based copyrighted function. Then, we observe the simple yet crucial relation between (public-key) copyrighted encryption and (public-key) traitor tracing, which we exploit by introducing a generic design paradigm for designing constant transmission rate traitor tracing schemes based on copyrighted encryption functions. Our first scheme achieves the same expansion efficiency as regular ElGamal encryption. The second scheme introduces only a slightly larger (constant) overhead, however, it additionally achieves efficient black-box traitor tracing (against any pirate construction).

Traitor Tracing with constant transmission rate

This paper shows a generic and simple conversion from weak asymmetric and symmetric encryption schemes into an asymmetric encryption scheme which is secure in a very strong sense- indistinguishability against adaptive chosen-ciphertext attacks in the random oracle model. In particular, this conversion can be applied efficiently to an asymmetric encryption scheme that provides a large enough coin space and, for every message, many enough variants of the encryption, like the ElGamal encryption scheme.

Secure integration of asymmetric and symmetric encryption schemes

The Fujisaki-Okamoto (FO) transformation (CRYPTO 1999 and Journal of Cryptology 2013) turns any weakly secure public-key encryption scheme into a strongly (i.e., \(\mathsf {IND}\text {-}\mathsf {CCA}\)) secure one in the random oracle model. Unfortunately, the FO analysis suffers from several drawbacks, such as a non-tight security reduction, and the need for a perfectly correct scheme. While several alternatives to the FO transformation have been proposed, they have stronger requirements, or do not obtain all desired properties.

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A Modular Analysis of the Fujisaki-Okamoto Transformation

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

In this paper we present efficient implementations of McEliece variants using quasi-dyadic codes. We provide secure parameters for a classical McEliece encryption scheme based on quasi-dyadic generalized Srivastava codes, and successively convert our scheme to a CCA2-secure protocol in the random oracle model applying the Fujisaki-Okamoto transform. In contrast with all other CCA2-secure code-based cryptosystems that work in the random oracle model, our conversion does not require a constant weight encoding function. We present results for both 128-bit and 80-bit security level, and for the latter we also feature an implementation for an embedded device.

/pdf/efficient-implementation-of-a-cca2-secure-variant-of-ydpf4hraf6.pdf

Efficient implementation of a CCA2-Secure variant of mceliece using generalized srivastava codes

Current widely-used key exchange (KE) mechanisms will be vulnerable to quantum attacks when sufficiently strong quantum computers become available. Therefore, devising quantum-resistant replacements that combine efficiency with solid security guarantees is an important and challenging task. This paper proposes several contributions towards this goal. First, we introduce “CAKE”, a key encapsulation algorithm based on the QC-MDPC McEliece encryption scheme, with two major improvements: (a) the use of ephemeral keys that defeats a recent reaction attack against MDPC decoding of the corresponding encryption scheme and (b) a highly efficient key generation procedure for QC-MDPC-based cryptosystems. Then, we present an authenticated key exchange protocol based on CAKE, which is suitable for the Internet Key Exchange (IKE) standard. We prove that CAKE is IND-CPA secure, that the protocol is SK-Secure, and suggest practical parameters. Compared to other post-quantum schemes, we believe that CAKE is a promising candidate for post-quantum key exchange standardization.

https://hal.inria.fr/hal-01661949/document

CAKE: Code-based Algorithm for Key Encapsulation

Recent public-key cryptography is largely based on number theory problems, such as factoring or computing of discrete logarithm. These systems constitute an excellent choice in many applications, and their security is well defined and understood. One of the major drawbacks, though, is that they will be vulnerable once quantum computers of an appropriate size are available. There is then a strong need for alternative systems that would resist attackers equipped with quantum technology. One of the most well-known systems of this kind is the McEliece cryptosystem, introduced in 1978, that is based on algebraic coding theory. There are no known vulnerabilities against quantum computers, and it has a very fast and efficient encryption procedure. However, it has also one big aw, the size of the public key, that makes it impractical for many applications. The first part of this thesis is dedicated to finding a way to significantly reduce the size of the public key. Latest publications achieve very good results by using codes with particular structures, obtaining keys as small as 4,096 bits. Unfortunately, almost all of the variants presented until now have been broken or proven to be insecure against the so-called structural attacks, i.e. attacks that aim to exploit the hidden structure in order to recover the private key. My work is based on Generalized Srivastava codes and represents a generalization of the Quasi-Dyadic scheme proposed by Misoczki and Barreto, with two advantages: a better flexibility, and improved resistance to all the known attacks. An efficient implementation of the above scheme is also provided, as a result of a joint work with P.-L. Cayrel and G. Hoffmann. In the next chapters, other important aspects of code-based cryptography are investigated. These include the study of a higher security standard, called indistinguishability under a chosen ciphertext attack, in the standard model, and the design of a code-based key encapsulation mechanism (KEM), which is an essential component of the hybrid encryption protocol. The last chapter is about digital signatures, a fundamental protocol in modern cryptography; existing code-based signatures schemes are reviewed and a negative result is obtained, showing that the design of an efficient signature scheme based on coding theory is still an open problem.

Improving the Efficiency of Code-Based Cryptography

Cryptographic schemes based on coding theory are one of the most accredited choices for cryptography in a post-quantum scenario. In this work, we present a hybrid construction based on the Niederreiter framework that provides IND-CCA security in the random oracle model. In addition, the construction satisfies the IK-CCA notion of anonymity whose importance is ever growing in the cryptographic community.

Secure and Anonymous Hybrid Encryption from Coding Theory

Code-based cryptographic schemes are highly regarded among the quantum-safe alternatives to current standards. Yet, designing code-based signatures using traditional methods has always been a challenging task, and current proposals are still far from the target set by other post-quantum primitives (e.g. lattice-based). In this paper, we revisit a recent work using an innovative approach for signing, based on the hardness of the code equivalence problem. We introduce some optimizations and provide a security analysis for all variants considered. We then show that the new parameters produce instances of practical interest.

Edoardo Persichetti

Papers

Efficient implementation of a CCA2-Secure variant of mceliece using generalized srivastava codes

CAKE: Code-based Algorithm for Key Encapsulation

Improving the Efficiency of Code-Based Cryptography

Secure and Anonymous Hybrid Encryption from Coding Theory

LESS-FM: Fine-Tuning Signatures from the Code Equivalence Problem