Chosen-ciphertext security from subset sum

We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012

A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

The zheng-seberry public key cryptosystem and signcryption

In 1993 Zheng-Seberry presented a public key cryptosystem that was considered efficient and secure in the sense of indistinguishability of encryptions (IND) against an adaptively chosen ciphertext adversary (CCA2). This thesis shows the Zheng-Seberry scheme is not secure as a CCA2 adversary can break the scheme in the sense of IND. In 1998 Cramer-Shoup presented a scheme that was secure against an IND-CCA2 adversary and whose proof relied only on standard assumptions. This thesis modifies this proof and applies it to a modified version of the El-Gamal scheme. This resulted in a provably secure scheme relying on the Random Oracle (RO) model, which is more efficient than the original Cramer-Shoup scheme. Although the RO model assumption is needed for security of this new El-Gamal variant, it only relies on it in a minimal way

A new cramer-shoup like methodology for group based provably secure encryption schemes

Proceedings of: TCC 2005: Theory of Cryptography Conference, 10-12 February 2005, Cambridge, MA, USA.A theoretical framework for the design of - in the sense of IND-CCA - provably secure public key cryptosystems taking non-abelian groups as a base is given. Our construction is inspired by Cramer and Shoup's general framework for developing secure encryption schemes from certain language membership problems; thus all our proofs are in the standard model, without any idealization assumptions. The skeleton we present is conceived as a guiding tool towards the construction of secure concrete schemes from finite non-abelian groups (although it is possible to use it also in conjunction with finite abelian groups)

A Like ELGAMAL Cryptosystem But Resistant To Post-Quantum Attacks

The Modulo 1 Factoring Problem (M1FP) is an elegant mathematical problem which could be exploited to design safe cryptographic protocols and encryption schemes that resist to post quantum attacks. The ELGAMAL encryption scheme is a well-known and efficient public key algorithm designed by Taher ELGAMAL from discrete logarithm problem. It is always highly used in Internet security and many other applications after a large number of years. However, the imminent arrival of quantum computing threatens the security of ELGAMAL cryptosystem and impose to cryptologists to prepare a resilient algorithm to quantum computer-based attacks. In this paper we will present a like-ELGAMAL cryptosystem based on the M1FP NP-hard problem. This encryption scheme is very simple but efficient and supposed to be resistant to post quantum attacks

Cryptosystems Resilient to Both Continual Key Leakages and Leakages from Hash Functions

Yoneyama et al. introduced Leaky Random Oracle Model (LROM for short) at ProvSec2008 in order to discuss security (or insecurity) of cryptographic schemes which use hash functions as building blocks when leakages from pairs of input and output of hash functions occur. This kind of leakages occurs due to various attacks caused by sloppy usage or implementation. Their results showed that this kind of leakages may threaten the security of some cryptographic schemes. However, an important fact is that such attacks would leak not only pairs of input and output of hash functions, but also the secret key. Therefore, LROM is rather limited in the sense that it considers leakages from pairs of input and output of hash functions alone, instead of taking into consideration other possible leakages from the secret key simultaneously. On the other hand, many other leakage models mainly concentrate on leakages from the secret key and ignore leakages from hash functions for a cryptographic scheme exploiting hash functions in these leakage models. Some examples show that the above drawbacks of LROM and other leakage models may cause insecurity of some schemes which are secure in the two kinds of leakage model. In this paper, we present an augmented model of both LROM and some leakage models, which both the secret key and pairs of input and output of hash functions can be leaked. Furthermore, the secret key can be leaked continually during the whole life cycle of a cryptographic scheme. Hence, our new model is more universal and stronger than LROM and some leakage models (e.g. only computation leaks model and bounded memory leakage model). As an application example, we also present a public key encryption scheme which is provably IND-CCA secure in our new model

Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack

Public-Key Encryption Schemes with Auxiliary Inputs

7th Theory of Cryptography Conference, TCC 2010, Zurich, Switzerland, February 9-11, 2010. ProceedingsWe construct public-key cryptosystems that remain secure even when the adversary is given any computationally uninvertible function of the secret key as auxiliary input (even one that may reveal the secret key information-theoretically). Our schemes are based on the decisional Diffie-Hellman (DDH) and the Learning with Errors (LWE) problems. As an independent technical contribution, we extend the Goldreich-Levin theorem to provide a hard-core (pseudorandom) value over large fields.National Science Foundation (U.S.) (Grant CCF-0514167)National Science Foundation (U.S.) (Grant CCF-0635297)National Science Foundation (U.S.) (Grant NSF-0729011)Israel Science Foundation (700/08)Chais Family Fellows Progra