A New Related Message Attack on RSA

Abstract. Coppersmith, Franklin, Patarin, and Reiter show that given two RSA cryptograms x e mod N and (ax + b) e mod N for known constants a, b ∈ ZN, one can compute x in O(e log 2 e) ZN-operations with some positive error probability. We show that given e cryptograms ci ≡ (aix + bi) e mod N, i = 0, 1,...e − 1, for any known constants ai, bi ∈ ZN, one can deterministically compute x in O(e) ZN-operations that depend on the cryptograms, after a pre-processing that depends only on the constants. The complexity of the pre-processing is O(e log 2 e) ZNoperations, and can be amortized over many instances. We also consider a special case where the overall cost of the attack is O(e) ZN-operations. Our tools are borrowed from numerical-analysis and adapted to handle formal polynomials over finite-rings. To the best of our knowledge their use in cryptanalysis is novel.

Encrypted Shared Data Spaces

The deployment of Share Data Spaces in open, possibly hostile, environments arises the need of protecting the confidentiality of the data space content. Existing approaches focus on access control mechanisms that protect the data space from untrusted agents. The basic assumption is that the hosts (and their administrators) where the data space is deployed have to be trusted. Encryption schemes can be used to protect the data space content from malicious hosts. However, these schemes do not allow searching on encrypted data. In this paper we present a novel encryption scheme that allows tuple matching on completely encrypted tuples. Since the data space does not need to decrypt tuples to perform the search, tuple confidentiality can be guaranteed even when the data space is deployed on malicious hosts (or an adversary gains access to the host). Our scheme does not require authorised agents to share keys for inserting and retrieving tuples. Each authorised agent can encrypt, decrypt, and search encrypted tuples without having to know other agents’ keys. This is beneficial inasmuch as it simplifies the task of key management. An implementation of an encrypted data space based on this scheme is described and some preliminary performance results are given

Shared and Searchable Encrypted Data for Untrusted Servers

Current security mechanisms pose a risk for organisations that outsource their data management to untrusted servers. Encrypting and decrypting sensitive data at the client side is the normal approach in this situation but has high communication and computation overheads if only a subset of the data is required, for example, selecting records in a database table based on a keyword search. New cryptographic schemes have been proposed that support encrypted queries over encrypted data but all depend on a single set of secret keys, which implies single user access or sharing keys among multiple users, with key revocation requiring costly data re-encryption. In this paper, we propose an encryption scheme where each authorised user in the system has his own keys to encrypt and decrypt data. The scheme supports keyword search which enables the server to return only the encrypted data that satisfies an encrypted query without decrypting it. We provide two constructions of the scheme giving formal proofs of their security. We also report on the results of a prototype implementation. This research was supported by the UK’s EPSRC research grant EP/C537181/1. The authors would like to thank the members of the Policy Research Group at Imperial College for their support

Conscript Your Friends into Larger Anonymity Sets with JavaScript

We present the design and prototype implementation of ConScript, a framework for using JavaScript to allow casual Web users to participate in an anonymous communication system. When a Web user visits a cooperative Web site, the site serves a JavaScript application that instructs the browser to create and submit "dummy" messages into the anonymity system. Users who want to send non-dummy messages through the anonymity system use a browser plug-in to replace these dummy messages with real messages. Creating such conscripted anonymity sets can increase the anonymity set size available to users of remailer, e-voting, and verifiable shuffle-style anonymity systems. We outline ConScript's architecture, we address a number of potential attacks against ConScript, and we discuss the ethical issues related to deploying such a system. Our implementation results demonstrate the practicality of ConScript: a workstation running our ConScript prototype JavaScript client generates a dummy message for a mix-net in 81 milliseconds and it generates a dummy message for a DoS-resistant DC-net in 156 milliseconds.Comment: An abbreviated version of this paper will appear at the WPES 2013 worksho

Share with Care: Breaking E2EE in Nextcloud

Nextcloud is a leading cloud storage platform with more than 20 million users. Nextcloud offers an end-to-end encryption (E2EE) feature that is claimed to be able “to keep extremely sensitive data fully secure even in case of a full server breach”. They also claim that the Nextcloud server “has Zero Knowledge, that is, never has access to any of the data or keys in unencrypted form”. This is achieved by having encryption and decryption operations that are done using file keys that are only available to Nextcloud clients, with those file keys being protected by a key hierarchy that ultimately relies on long passphrases known exclusively to the users. We provide the first detailed documentation and security analysis of Nextcloud\u27s E2EE feature. Nextcloud\u27s strong security claims motivate conducting the analysis in the setting where the server itself is considered malicious. We present three distinct attacks against the E2EE security guarantees in this setting. Each one enables the confidentiality and integrity of all user files to be compromised. All three attacks are fully practical and we have built proof-of-concept implementations for each. The vulnerabilities make it trivial for a malicious Nextcloud server to access and manipulate users\u27 data. We have responsibly disclosed the three vulnerabilities to Nextcloud. The second and third vulnerabilities have been remediated. The first was addressed by temporarily disabling file sharing from the E2EE feature until a redesign of the feature can be made. We reflect on broader lessons that can be learned for designers of E2EE systems

Statistical Properties of Short RSA Distribution and Their Cryptographic Applications

International audienceIn this paper, we study some computational security assump-tions involve in two cryptographic applications related to the RSA cryp-tosystem. To this end, we use exponential sums to bound the statistical distances between these distributions and the uniform distribution. We are interesting studying the k least (or most) significant bits of x e mod N , where N is a RSA modulus when x is restricted to a small part of [0, N). First of all, we provide the first rigorous evidence that the cryptographic pseudo-random generator proposed by Micali and Schnorr is based on firm foundations. This proof is missing in the original paper and do not cover the parameters chosen by the authors. Consequently, we extend the proof to get a new result closer to the parameters using a recent work of Wooley on exponential sums and we show some limitations of our technique. Finally, we look at the semantic security of the RSA padding scheme called PKCS#1 v1.5 which is still used a lot in practice. We show that parts of the ciphertexts are indistinguisable from uniform bitstrings