The Random Oracle Methodology, Revisited

We take a critical look at the relationship between the security of cryptographic schemes in the Random Oracle Model, and the security of the schemes that result from implementing the random oracle by so called "cryptographic hash functions". The main result of this paper is a negative one: There exist signature and encryption schemes that are secure in the Random Oracle Model, but for which any implementation of the random oracle results in insecure schemes. In the process of devising the above schemes, we consider possible definitions for the notion of a "good implementation" of a random oracle, pointing out limitations and challenges.Comment: 31 page

Theory and practice of secret commitment

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 77-80).by Shai Halevi.Ph.D

Graded Encoding, Variations on a Scheme

In this note we provide a more-or-less unified framework to talk about the functionality and security of graded encoding schemes, describe some variations of recent schemes, and discuss their security. In particular we describe schemes that combine elements from both the GGH13 scheme of Garg, Gentry and Halevi (EUROCRYPT 2013) and the GGH15 scheme of Gentry, Gorbunov and Halevi (TCC 2015). On one hand, we show how to use techniques from GGH13 in the GGH15 construction to enable encoding of arbitrary plaintext elements (as opposed to only small ones) and to introduce levels/subsets (e.g., as needed to implement straddling sets). On the other hand, we show how to modify the GGH13 scheme to support graph-induced constraints (either instead of, or in addition to, the levels from GGH13). Turning to security, we describe zeroizing attacks on the GGH15 scheme, similar to those described by Cheon et al. (EUROCRYPT 2015) and Coron et al. (CRYPTO 2015) on the CLT13 and GGH13 constructions. As far as we know, however, these attacks to not break the GGH15 multi-partite key-agreement protocol. We also describe a new multi-partite key-agreement protocol using the GGH13 scheme, which also seems to resist known attacks. That protocol suggests a relatively simple hardness assumption for the GGH13 scheme, that we put forward as a target for cryptanalysis

EME*: extending EME to handle arbitrary-length messages with associated data

This work describes a mode of operation, EME*, that turns a regular block cipher into a length-preserving enciphering scheme for messages of (almost) arbitrary length. Specifically, the resulting scheme can handle any bit-length, not shorter than the block size of the underlying cipher, and it also handles associated data of arbitrary bit-length. Such a scheme can either be used directly in applications that need encryption but cannot afford length expansion, or serve as a convenient building block for higher-level modes. The mode EME* is a refinement of the EME mode of Halevi and Rogaway, and it inherits the efficiency and parallelism from the original EME

A sufficient condition for key-privacy

The notion of key privacy for encryption schemes was defined formally by Bellare, Boldyreva, Desai and Pointcheval in Asiacrypt 2001. This notion seems useful in settings where anonymity is important. In this short note we describe a (very simple) sufficient condition for key privacy. In a nutshell, a scheme that provides data privacy is guaranteed to provide also key privacy if the distribution of a *random encryption of a random message* is independent of the public key that is used for the encryption

The random oracle methodology, revisited

We take a critical look at the relationship between the security of cryptographic schemes in the Random Oracle Model, and the security of the schemes that result from implementing the random oracle by so called “cryptographic hash functions”. The main result of this paper is a negative one: There exist signature and encryption schemes that are secure in the Random Oracle Model, but for which any implementation of the random oracle results in insecure schemes. In the process of devising the above schemes, we consider possible definitions for the notion of a “good implementation” of a random oracle, pointing out limitations and challengesAccepted manuscrip

Weighted Secret Sharing from Wiretap Channels

Secret-sharing allows splitting a piece of secret information among a group of shareholders, so that it takes a large enough subset of them to recover it. In weighted secret-sharing, each shareholder has an integer weight, and it takes a subset of large-enough weight to recover the secret. Schemes in the literature for weighted threshold secret sharing either have share sizes that grow linearly with the total weight, or ones that depend on huge public information (essentially a garbled circuit) of size (quasi)polynomial in the number of parties. To do better, we investigate a relaxation, (?, ?)-ramp weighted secret sharing, where subsets of weight ? W can recover the secret (with W the total weight), but subsets of weight ? W or less cannot learn anything about it. These can be constructed from standard secret-sharing schemes, but known constructions require long shares even for short secrets, achieving share sizes of max(W,|secret|/?), where ? = ?-?. In this note we first observe that simple rounding let us replace the total weight W by N/?, where N is the number of parties. Combined with known constructions, this yields share sizes of O(max(N,|secret|)/?). Our main contribution is a novel connection between weighted secret sharing and wiretap channels, that improves or even eliminates the dependence on N, at a price of increased dependence on 1/?. We observe that for certain additive-noise (?,?) wiretap channels, any semantically secure scheme can be naturally transformed into an (?,?)-ramp weighted secret-sharing, where ?,? are essentially the respective capacities of the channels ?,?. We present two instantiations of this type of construction, one using Binary Symmetric wiretap Channels, and the other using additive Gaussian Wiretap Channels. Depending on the parameters of the underlying wiretap channels, this gives rise to (?, ?)-ramp schemes with share sizes |secret|?log N/poly(?) or even just |secret|/poly(?)

Many-to-one Trapdoor Functions and Their Relation to Public-Key Cryptosystems

The heart of the task of building public key cryptosystems is viewed as that of "making trapdoors;" in fact, public key cryptosystems and trapdoor functions are often discussed as synonymous. How accurate is this view? In this paper we endeavor to get a better understanding of the nature of "trapdoorness" and its relation to public key cryptosystems, by broadening the scope of the investigation: we look at general trapdoor functions; that is, functions that are not necessarily injective (ie., one-to-one). Our first result is somewhat surprising: we show that non-injective trapdoor functions (with super-polynomial pre-image size) can be constructed from any one-way function (and hence it is unlikely that they suffice for public key encryption). On the other hand, we show that trapdoor functions with polynomial pre-image size are sufficient for public key encryption. Together, these two results indicate that the pre-image size is a fundamental parameter of trapdoor functions. We then turn our attention to the converse, asking what kinds of trapdoor functions can be constructed from public key cryptosystems. We take a first step by showing that in the random-oracle model one can construct injective trapdoor functions from any public key cryptosystem.Engineering and Applied Science

Bootstrapping for HElib

Gentry\u27s bootstrapping technique is still the only known method of obtaining fully homomorphic encryption where the system\u27s parameters do not depend on the complexity of the evaluated functions. Bootstrapping involves a *recryption* procedure where the scheme\u27s decryption algorithm is evaluated homomorphically. Prior to this work there were very few implementations of recryption, and fewer still that can handle ``packed ciphertexts\u27\u27 that encrypt vectors of elements. In the current work, we report on an implementation of recryption of fully-packed ciphertexts using the HElib library for somewhat-homomorphic encryption. This implementation required extending previous recryption algorithms from the literature, as well as many aspects of the HElib library. Our implementation supports bootstrapping of packed ciphertexts over many extension fields/rings. One example that we tested involves ciphertexts that encrypt vectors of 1024 elements from $GF(2^{16})$. In that setting, the recryption procedure takes under 3 minutes (at security-level $\approx 80$) on a single core, and allows a multiplicative depth-11 computation before the next recryption is needed. This report updates the results that we reported in Eurocrypt 2015 in several ways. Most importantly, it includes a much more robust method for deriving the parameters, ensuring that recryption errors only occur with negligible probability. Many aspects of this analysis are proven, and for the few well-specified heuristics that we made, we report on thorough experimentation to validate them. The procedure that we describe here is also significantly more efficient than in the previous version, incorporating many optimizations that were reported elsewhere (such as more efficient linear transformations) and adding a few new ones. Finally, our implementation now also incorporates Chen and Han\u27s techniques from Eurocrypt 2018 for more efficient digit extraction (for some parameters), as well as for ``thin bootstrapping\u27\u27 when the ciphertext is only sparsely packed

Random-Index Oblivious RAM

We study the notion of Random-index ORAM (RORAM), which is a weak form of ORAM where the Client is limited to asking for (and possibly modifying) random elements of the $N$-items memory, rather than specific ones. That is, whenever the client issues a request, it gets in return a pair $(r,x_r)$ where $r\in_R[N]$ is a random index and $x_r$ is the content of the $r$-th memory item. Then, the client can also modify the content to some new value $x\u27_r$. We first argue that the limited functionality of RORAM still suffices for certain applications. These include various applications of sampling (or sub-sampling), and in particular the very-large-scale MPC application in the setting of~ Benhamouda et al. (TCC 2020). Clearly, RORAM can be implemented using any ORAM scheme (by the Client selecting the random $r$\u27s by himself), but the hope is that the limited functionality of RORAM can make it faster and easier to implement than ORAM. Indeed, our main contributions are several RORAM schemes (both of the hierarchical-type and the tree-type) of lighter complexity than that of ORAM