Security of discrete log cryptosystems in the random oracle and the generic model

We introduce novel security proofs that use combinatorial counting arguments rather than reductions to the discrete logarithm or to the Diffie-Hellman problem. Our security results are sharp and clean with no polynomial reduction times involved. We consider a combination of the random oracle model and the generic model. This corresponds to assuming an ideal hash function H given by an oracle and an ideal group of prime order q, where the binary encoding of the group elements is useless for cryptographic attacks In this model, we first show that Schnorr signatures are secure against the one-more signature forgery : A generic adversary performing t generic steps including l sequential interactions with the signer cannot produce l+1 signatures with a better probability than (t 2)/q. We also characterize the different power of sequential and of parallel attacks. Secondly, we prove signed ElGamal encryption is secure against the adaptive chosen ciphertext attack, in which an attacker can arbitrarily use a decryption oracle except for the challenge ciphertext. Moreover, signed ElGamal encryption is secure against the one-more decryption attack: A generic adversary performing t generic steps including l interactions with the decryption oracle cannot distinguish the plaintexts of l + 1 ciphertexts from random strings with a probability exceeding (t 2)/q

Security of signed ELGamal encryption

Assuming a cryptographically strong cyclic group G of prime order q and a random hash function H, we show that ElGamal encryption with an added Schnorr signature is secure against the adaptive chosen ciphertext attack, in which an attacker can freely use a decryption oracle except for the target ciphertext. We also prove security against the novel one-more-decyption attack. Our security proofs are in a new model, corresponding to a combination of two previously introduced models, the Random Oracle model and the Generic model. The security extends to the distributed threshold version of the scheme. Moreover, we propose a very practical scheme for private information retrieval that is based on blind decryption of ElGamal ciphertexts

A Type-and-Identity-based Proxy Re-Encryption Scheme and its Application in Healthcare

Proxy re-encryption is a cryptographic primitive developed to delegate the decryption right from one party (the delegator) to another (the delegatee). In a proxy re-encryption scheme, the delegator assigns a key to a proxy to re-encrypt all messages encrypted with his public key such that the re-encrypted ciphertexts can be decrypted with the delegatee’s private key. We propose a type-and-identity-based proxy re-encryption scheme based on the Boneh-Franklin Identity Based Encryption (IBE) scheme. In our scheme, the delegator can categorize messages into different types and delegate the decryption right of each type to the delegatee through a proxy. Our scheme enables the delegator to provide the proxy fine-grained re-encryption capability. As an application, we propose a fine-grained Personal Health Record (PHR) disclosure scheme for healthcare service by applying the proposed scheme

Cast-as-Intended Mechanism with Return Codes Based on PETs

We propose a method providing cast-as-intended verifiability for remote electronic voting. The method is based on plaintext equivalence tests (PETs), used to match the cast ballots against the pre-generated encrypted code tables. Our solution provides an attractive balance of security and functional properties. It is based on well-known cryptographic building blocks and relies on standard cryptographic assumptions, which allows for relatively simple security analysis. Our scheme is designed with a built-in fine-grained distributed trust mechanism based on threshold decryption. It, finally, imposes only very little additional computational burden on the voting platform, which is especially important when voters use devices of restricted computational power such as mobile phones. At the same time, the computational cost on the server side is very reasonable and scales well with the increasing ballot size

Privacy preserving distributed optimization using homomorphic encryption

This paper studies how a system operator and a set of agents securely execute a distributed projected gradient-based algorithm. In particular, each participant holds a set of problem coefficients and/or states whose values are private to the data owner. The concerned problem raises two questions: how to securely compute given functions; and which functions should be computed in the first place. For the first question, by using the techniques of homomorphic encryption, we propose novel algorithms which can achieve secure multiparty computation with perfect correctness. For the second question, we identify a class of functions which can be securely computed. The correctness and computational efficiency of the proposed algorithms are verified by two case studies of power systems, one on a demand response problem and the other on an optimal power flow problem.Comment: 24 pages, 5 figures, journa

Public Key Encryption Supporting Plaintext Equality Test and User-Specified Authorization

In this paper we investigate a category of public key encryption schemes which supports plaintext equality test and user-specified authorization. With this new primitive, two users, who possess their own public/private key pairs, can issue token(s) to a proxy to authorize it to perform plaintext equality test from their ciphertexts. We provide a formal formulation for this primitive, and present a construction with provable security in our security model. To mitigate the risks against the semi-trusted proxies, we enhance the proposed cryptosystem by integrating the concept of computational client puzzles. As a showcase, we construct a secure personal health record application based on this primitive

Secure Integer Comparisons Using the Homomorphic Properties of Prime Power Subgroups

Secure multi party computation allows two or more parties to jointly compute a function under encryption without leaking information about their private inputs. These secure computations are vital in many fields including law enforcement, secure voting and bioinformatics because the privacy of the information is of paramount importance. One common reference problem for secure multi party computation is the Millionaires\u27 problem which was first introduced by Turing Award winner Yao in his paper Protocols for secure computation . The Millionaires\u27 problem considers two millionaires who want to know who is richer without disclosing their actual worth. There are public-key cryptosystems that currently solve this problem, however they use bitwise decomposition and Boolean algebra on encrypted bits. This type of solution is costly as it requires each bit requires its own encryption and decryption. Our solution to the Millionaires\u27 problem and secure integer comparison looks at a new approach which doesn\u27t use the decomposition method and instead encrypts the full length of the message in one encryption (within scope). This method also extends in a linear fashion, so larger integers remain efficient to compare. In this thesis, we present a new cryptosystem with a novel homomorphic property used for secure integer comparison, as well as a protocol implementing the cryptosystem and a simulation security proof for the protocol. Finally, we implemented the system and compared it to systems that are being used today