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

In this chapter we provide an overview of the concept of blockchain technology and its potential to disrupt the world of banking through facilitating global money remittance, smart contracts, automated banking ledgers and digital assets. In this regard, we first provide a brief overview of the core aspects of this technology, as well as the second-generation contract-based developments. From there we discuss key issues that must be considered in developing such ledger based technologies in a banking context.

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Understanding Modern Banking Ledgers Through Blockchain Technologies: Future of Transaction Processing and Smart Contracts on the Internet of Money

Garbled circuits, a classical idea rooted in the work of Yao, have long been understood as a cryptographic technique, not a cryptographic goal. Here we cull out a primitive corresponding to this technique. We call it a garbling scheme. We provide a provable-security treatment for garbling schemes, endowing them with a versatile syntax and multiple security definitions. The most basic of these, privacy, suffices for two-party secure function evaluation (SFE) and private function evaluation (PFE). Starting from a PRF, we provide an efficient garbling scheme achieving privacy and we analyze its concrete security. We next consider obliviousness and authenticity, properties needed for private and verifiable outsourcing of computation. We extend our scheme to achieve these ends. We provide highly efficient blockcipher-based instantiations of both schemes. Our treatment of garbling schemes presages more efficient garbling, more rigorous analyses, and more modularly designed higher-level protocols.

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Foundations of garbled circuits

In this paper we prove that the sponge construction introduced in [4] is indifferentiable from a random oracle when being used with a random transformation or a random permutation and discuss its implications. To our knowledge, this is the first time indifferentiability has been shown for a construction calling a random permutation (instead of an ideal compression function or ideal block cipher) and for a construction generating outputs of any length (instead of a fixed length).

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On the indifferentiability of the sponge construction

The most common way of constructing a hash function (e.g., SHA-1) is to iterate a compression function on the input message. The compression function is usually designed from scratch or made out of a block-cipher. In this paper, we introduce a new security notion for hash-functions, stronger than collision-resistance. Under this notion, the arbitrary length hash function H must behave as a random oracle when the fixed-length building block is viewed as a random oracle or an ideal block-cipher. The key property is that if a particular construction meets this definition, then any cryptosystem proven secure assuming H is a random oracle remains secure if one plugs in this construction (still assuming that the underlying fixed-length primitive is ideal). In this paper, we show that the current design principle behind hash functions such as SHA-1 and MD5 — the (strengthened) Merkle-Damgard transformation — does not satisfy this security notion. We provide several constructions that provably satisfy this notion; those new constructions introduce minimal changes to the plain Merkle-Damgard construction and are easily implementable in practice.

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Merkle-Damgård revisited: how to construct a hash function

We propose a new mode of operation, enciphered CBC, for domain extension of length-preserving functions (like block ciphers), which is a variation on the popular CBC mode of operation. Our new mode is twice slower than CBC, but has many (property-preserving) properties not enjoyed by CBC and other known modes. Most notably, it yields the first constant-rate Variable Input Length (VIL) MAC from any length preserving Fixed Input Length (FIL) MAC. This answers the question of Dodis and Puniya from Eurocrypt 2007. Further, our mode is a secure domain extender for PRFs (with basically the same security as encrypted CBC). This provides a hedge against the security of the block cipher: if the block cipher is pseudorandom, one gets a VIL-PRF, while if it is "only" unpredictable, one "at least" gets a VIL-MAC. Additionally, our mode yields a VIL random oracle (and, hence, a collision-resistant hash function) when instantiated with length-preserving random functions, or even random permutations (which can be queried from both sides). This means that one does not have to re-key the block cipher during the computation, which was critically used in most previous constructions (analyzed in the ideal cipher model).

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A new mode of operation for block ciphers and length-preserving MACs

The Random Oracle Model and the Ideal Cipher Model are two of the most popular idealized models in cryptography. It is a fundamentally important practical and theoretical problem to compare the relative strengths of these models and to see how they relate to each other. Recently, Coron et al. [8] proved that one can securely instantiate a random oracle in the ideal cipher model. In this paper, we investigate if it is possible to instantiate an ideal block cipher in the random oracle model, which is a considerably more challenging question. We conjecture that the Luby-Rackoff construction [19] with a sufficient number of rounds should suffice to show this implication. This does not follow from the famous Luby-Rackoff result [19] showing that 4 rounds are enough to turn a pseudorandom function into a pseudorandom permutation, since the results of the intermediate rounds are known to everybody. As a partial step toward resolving this conjecture, we show that random oracles imply ideal ciphers in the honest-but-curious model, where all the participants are assumed to follow the protocol, but keep all their intermediate results. Namely, we show that the Luby-Rackoff construction with a superlogarithmic number of rounds can be used to instantiate the ideal block cipher in any honest-but-curious cryptosystem, and result in a similar honest-but-curious cryptosystem in the random oracle model. We also show that securely instantiating the ideal cipher using the Luby Rackoff construction with upto a logarithmic number of rounds is equivalent in the honest-but-curious and malicious models.

On the relation between the ideal cipher and the random oracle models

Feistel Network, consisting of a repeated application of the Feistel Transform, gives a very convenient and popular method for designing "cryptographically strong" permutations from corresponding "cryptographically strong" functions. Up to now, all usages of the Feistel Network, including the celebrated Luby-Rackoff's result, critically rely on (a) the (pseudo)randomness of round functions; and (b) the secrecy of (at least some of) the intermediate round valuesappearing during the Feistel computation. Moreover, a small constant number of Feistel rounds was typically sufficient to guarantee security under assumptions (a) and (b). In this work we consider several natural scenarios where at least one of the above assumptions does not hold, and show that a constant, or even logarithmic number of rounds is provably insufficientto handle such applications, implying that a new method of analysis is needed.

On a positive side, we develop a new combinatorial understanding of Feistel networks, which makes them applicable to situations when the round functions are merely unpredictablerather than (pseudo)random and/or when the intermediate round values may be leaked to the adversary (either through an attack or because the application requiresit). In essence, our results show that in any such scenario a super-logarithmic number of Feistel rounds is necessary and sufficientto guarantee security.

Of independent interest, our technique yields a novel domain extension method for messages authentication codes and other related primitives, settling a question studied by An and Bellare in CRYPTO 1999.

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Feistel Networks Made Public, and Applications

Cascade chaining is a very efficient and popular mode of operation for building various kinds of cryptographic hash functions. In particular, it is the basis of the most heavily utilized SHA function family. Recently, many researchers pointed out various practical and theoretical deficiencies of this mode, which resulted in a renewed interest in building specialized modes of operations and new hash functions with better security. Unfortunately, it appears unlikely that a new hash function (say, based on a new mode of operation) would be widely adopted before being standardized, which is not expected to happen in the foreseeable future.

Instead, it seems likely that practitioners would continue to use the cascade chaining, and the SHA family in particular, and try to work around the deficiencies mentioned above. In this paper we provide a thorough treatment of how to soundly design a secure hash function H′ from a given cascade-based hash function H for various cryptographic applications, such as collision-resistance, one-wayness, pseudorandomness, etc. We require each proposed construction of HH′ to satisfy the following "axioms". 1. The construction consists of one or two "black-box" calls to H. 2. In particular, one is not allowed to know/use anything about the internals of H, such as modifying the initialization vector or affecting the value of the chaining variable. 3. The construction should support variable-length inputs. 4. Compared to a single evaluation of H(M), the evaluation of H(M) should make at most a fixed (small constant) number of extra calls to the underlying compression function of H. In other words, the efficiency of H′ is negligibly close to that of H.

We discuss several popular modes of operation satisfying the above axioms. For each such mode and for each given desired security requirement, we discuss the weakest requirement on the compression function of H which would make this mode secure. We also give the implications of these results for using existing hash functions SHA-x, where x ∈ {1, 224, 256, 384, 512}.

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Prashant Puniya

Papers

Merkle-Damgård revisited: how to construct a hash function

A new mode of operation for block ciphers and length-preserving MACs

On the relation between the ideal cipher and the random oracle models

Feistel Networks Made Public, and Applications

Getting the best out of existing hash functions; or what if we are stuck with SHA?