There are several other variants. In A. Odlyzko, editor, Y. Frankel, Y. Tsiounis, and M. Yung. The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption. Moreover, we construct a homomorphic verification scheme above tree structure to solve the privacy leakage problem in third-party audit. Towards Practical Public Key Systems Secure Against Chosen Ciphertext Attacks. The secret key is x and the public key is {y, g, p}. The ElGamal encryption is leveraged to encrypt the private data before uploading. We illustrate via two simple case studies and on a voting protocol. A combination of IFP and DLP is proposed. How to prove yourself: Practical solutions to identification and signature problems. 4 On the Security of a Variant of ElGamal Encryption Scheme. For, above (“lunch-time attack” [NY90]) provides no information to the adversary, if, she has produced the ciphertexts by herself. To solve these problems, we propose a new authenticate data structure named privacy-preserving adaptive trapdoor hash authentication tree (P-ATHT) by introducing trapdoor hash and BLS signature to the Merkle hash tree. However, its security has never been concretely proven based on clearly understood and accepted primitives. M. Bellare and P. Rogaway. All rights reserved. Furthermore, this proposed work illustrates a security proof of the proposed schemes and shows that the presented schemes are well protected in the modern computing environment. The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes. It was described by Taher Elgamal in 1985. On the construction of pseudo-random permutations: Luby-Rackoff revisited. chosen ciphertext attack under standard intractability assumptions. Download preview PDF. In conceptual modelling, context-awareness should be precisely highlighted. Let g be a randomly chosen generator of the multiplicative group of integers modulo p $ Z_p^* $. However, its security has never been concretely proven based on clearly understood and accepted primitives. By utilizing the ElGamal encryption, the server learns nearly nothing about the private data or the statistical result. It was described by Taher Elgamal in 1984. The scheme uses three cryptographic primitives: In A. The in-, ﬁed adversarial algorithm which: (1) constructs a random oracle, the adversary until she produces a forged signature (, adversary on the same inputs; (3) outputs the private key, the Schnorr signature, and from this computes, other words, if the adversary can produce a signature, then it is withi, computational power (via the modiﬁcation above) to compute the private key, ing oracle then the assumption holds [PS96]. Our proof employs the tool of message awareness. On the Security of ElGamal Based Encryption - The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes. I. Towards realizing random oracles: Hash functions that hide all partial information. ... (For ElGamal, the extractor would extract the randomness x used to produce (X = xG, Z = M + xY ) from the proof of knowledge and return the plaintext M = Z − xY .) Springer-Verlag, 1987. on non-interactive zero-knowledge proof of knowledge to be secure against it. Efficient signature generation by smart cards. In this paper we introduce a new approach of constructing time capsule signature. A public key cryptosystem and a signature scheme based on discrete logarithms. In. Extensive experiments are conducted to demonstrate the high efficiency of FairCrowd for aggregate statistics in mobile crowdsensing. The only known security proof is informal and in the combination of the generic group model (GGM) and the random oracle model (ROM) assuming that the “ROS problem” is hard. In this paper, an alternative public-key cryptosystems (PKCs) are proposed based on the new algebraic problems namely “Dependent RSA Discrete Logarithm Problems” derived from the RSA and Discrete Logarithm (DLog) assumptions together. The El Gamal encryption scheme [ElG8 5] is based on the Diﬃe-He llman assumpt ion and it is a probabilistic encryption sc heme, i.e., a speciﬁc … Foundations of cryptography, 1989. A comparison has been conducted for different public key encryption algorithms at different data size. O. Goldreich. ElGamal encryption can be defined over any cyclic group G. Its security depends upon the difficulty of a certain problem in G related to computing discrete logarithms. Public-key cryptosytems provably secure against chosen ciphertext attack. that enjoys both of these properties simultaneously. © 2020 Springer Nature Switzerland AG. ElGamal encryption is an public-key cryptosystem. one of the schemes proposed by Zheng-Seberry -which is based on ElGamal signature- by adapting Schnorr signature in order to enhance the e ciency and give a rigorous proof of security … The P-ATHAT scheme realizes real-time verification of data stream and can dynamically expand its structure as the data stream arrives. K. Sakurai and H. Shizuya. pm ∈ [21000,25000], and work with the ElGamal encryp-tion scheme based on an arbitrary subgroup of the multi-plicative group of GF(pm) with the key size 1000 – 5000 bits long. These PKCs are provably secure for the notions of security: indistinguishable encryptions under chosen-plaintext attacks (IND-CPA), and adaptive chosen-ciphertext attacks (IND-CCA2). The time capsule signature provides an elegant way to produce a "future signature" that be- comes valid from a specific future time t, when a trusted third party (called Time Server), The Pintsov-Vanstone signature scheme with partial message recovery (PVSSR) is a signature scheme with low message expansion Maybe of independent interest is a new efficient method to encrypt long messages exceeding the length of the permutation while retaining the minimal overhead. For this model, under suitable complexity assumptions, it is proved that extracting any information about the cleartext from the cyphertext is hard on the average for an adversary with polynomially bounded computational resources. Available at http://www.cs.wisc.edu/ shoup/papers/. Here we show directly that the decision Diffie-Hellman assumption implies the security of the original ElGamal encryption scheme (with messages from a subgroup) without modification. In U. Maurer, editor, C. Rackoff and D. Simon. Non-malleable cryptography. Idea of ElGamal cryptosystem The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes. ElGamal encryption is provably secure under CPA [19], and is insecure under CCA2. Finally, as we also note in the next section, proof of o, strate the scheme using Schnorr proofs of knowledge [Sch91] but other protocols, The idea here is that the sender sends a zero-knowledge (ZK) proof of knowl-, rather only as an unpredictable chellenge generator (the Fia, to the proofs of section 3. Notice that the main trick here is that the translator gets, forms a Schnorr signature on the message (, extracting the private key corresponding to, phrased more generally to cover all applications of Schnorr signatures. It uses asymmetric key encryption for communicating between two parties and encrypting the message. On the Security of ElGamal Based Encryption. Concretely, we show that it only holds if the underlying trapdoor permutation is certified. Hence, it becomes more efficient than all the cryptosystems specially designed for the ElGamal cryptosystem to make it indistinguishable encryptions under adaptive chosen-ciphertext attacks. such that the order of is a sufficiently large prime q, e.g., q 2140. Our protocol has effectively been deployed within a network of more than 5000 pharmacies. The experimental results show that the proposed scheme has lower overheads in communication and access as compared to the technique CDS. The difference between the length of a ciphertext and the embedded message is called the ciphertext overhead. Secondly, based on the proposed storage scheme and ElGamal encryption, we propose a lightweight access model for users to access the final data processed by cloud server. Non-Malleable Cryptography (Extended Abstract). Next we present additions on ElGamal encryption which result in non-malleability under adaptive chosen plaintext attacks. Optimal assymetric encryption â how to encrypt with RSA. Y. Tsiounis and M. Yung. Blind Schnorr Signatures and Signed ElGamal Encryption in the Algebraic Group Model, An alternative practical public-key cryptosystems based on the Dependent RSA Discrete Logarithm Problems, Private, Fair, and Verifiable Aggregate Statistics for Mobile Crowdsensing in Blockchain Era, A Data Storage and Sharing Scheme for Cyber-Physical-Social Systems, SGX-based Users Matching with Privacy Protection, Contextual Dependency in State-Based Modelling, Zero-Knowledge to the Rescue: Consistent Redundant Backup of Keys Generated for Critical Financial Services, Blind Transfer of Personal Data Achieving Privacy, An Adaptive Authenticated Data Structure With Privacy-Preserving for Big Data Stream in Cloud, About Asymmetric Execution of the Asymmetric ElGamal Cipher, Efficient signature generation by smart cards, Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack, Foundations of cryptography – a primer. A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack, 1998. Abstract: In this paper, we discuss the security of the ElGamal encryption scheme and its variant by Damgard. We present a new public-key signature scheme and a corresponding authentication scheme that are based on discrete logarithms in a subgroup of units in where p is a sufficiently large prime, e.g., p 2512. We present an efficient algorithm that preprocesses the exponentiation of a random residue modulo p. The zero-knowledge proof of knowledge, first defined by Fiat, Fiege and Shamir, was used by Galil, Haber and Yung as a means A new public key cryptosystem is proposed and analyzed. Immunizing public key cryptosystems against chosen ciphertext attacks. Y. Zheng and J. Seberry. 179, Santa Barbara, CA, August 17–21 1997. proposed a linear encryption scheme based on the El-Gamal encryption scheme. In. Our proof employs the tool of message awareness. Springer-V. ElGamal encryption is provably secure under CPA [10], and is insecure under CCA2. If she has not produced the cipher-, ciphertexts, then this is equivalent as having some a-priori information; this is, deciphering oracle the adversary already knows, has eﬀectively produced a Schnorr signature on the message (, eﬀect the sender only states a name and binds the encryption to that name, but, non-malleable (in our scheme a Schnorr signature can be added. The problem of breaking the ElGamal encryption scheme, i.e., recovering m given p,g,(g^x) and a, b is equivalent to solving the Diffie-Hellman problem (see x3.7). Over 10 million scientific documents at your fingertips. In Section 3, we review signed ElGamal encryption, which is based on the original ElGamal encryption. Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. ... To encrypt a message M ∈ G, one draws x ←$ Z p , computes X = xG, and outputs ciphertext (X, M + xY ). In this article, we address the problem of privacy when data containing sensitive information are processed by a third party. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. The situation is similar for (Schnorr-)signed ElGamal encryption, a simple CCA2-secure variant of ElGamal. D. Pointcheval and J. Stern. On the Security of a Variant of ElGamal Encryption Scheme Abstract: Recently, based on the Paillier cryptosystem [1] , Yi et al. In this architecture, it turned out, that the usually considered theoretical and costly transferable Zero-Knowledge proofs, actually help overcome the operational and integrity constraints. Exploitation of data for statistical or economic analyses is an important and rapidly growing area. A New Construction of Time Capsule Signature. I'll use Taher ElGamal's A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms (July 1985 in IEEE Transactions on Information Theory, formerly in proceedings of Crypto 1984) as the reference scheme. The proof holds for any message space with any probability distribution. Cyber-Physical-Social System (CPSS) provides users secure and high-quality mobile service applications to share and exchange data in the cyberspace and physical world. , where qs ElGamal … Non-malleability is equivalent to the decision Diffie-Hellman assumption, the existence of a random oracle (in practice a secure hash function) or a trusted beacon (as needed for the Fiat-Shamir argument), and one assumption about the unforgeability of Schnorr signatures. Formal Security Proofs for a Signature Scheme with Partial Message Recovery. We demonstrate this by presenting some additional adjustments of the construction that achieve the following: We present two efficient constructions aimed at making public key systems secure against chosen ciphertext attacks. C. P. Schnorr. In this way we improve the ElGamal signature scheme in the speed of the procedures for the generation and the verification of signatures and also in the bit length of signatures. Secure and Privacy-preserving Computation. A. Fiat and A. Shamir. In. Here we show directly that the decision, semantic security of the ElGamal encryption is actually, Next we present additions on ElGamal encryption, equivalent to the decision Diﬃe-Hellman assumption, the existence of a, bit commitments. proof makes a concrete, Every public-key encryption scheme has to incorporate a certain amount of randomness into its ciphertexts to provide semantic security against chosen ciphertext attacks (IND-CCA). But there are many differences between the schemes, especially when one looks at the the parameter choices. R. Cramer and V. Shoup. The second construction applies to the El Gamal/Diffie-Hellman public key system. 1 (2005), Optimal asymmetric encryption--how to encrypt with rsa, Practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. On the Security of ElGamal Based Encryption Yiannis Tsiounis1 and Moti Yung2 1 GTE Laboratories Inc., Waltham MA ytsiounis@gte.com 2 CertCo, NY, NY moti@certco.com Abstract. In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. , and for every probabilistic polynomial time algorithm. ) Relationships among the computational powers of breaking discrete log cryptosystems. While a generic brute-force adversary running in 2 t steps gives a theoretical lower bound of t bits on the, RSA Full Domain Hash (RSA-FDH) is a digital signature scheme, secure again chosen message attacks in the random oracle model. The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes. outline a distributed ElGamal cryptosystem which allows for both a much simpler distributed key generation procedure and a more efficient distributed decryption of messages from a large plaintext domain [2] . However, its security has never been concretely proven based on clearly understood and accepted primitives. However, most of these sub-protocols have not been shown, without a proof. These keys need to be trusted (random) and secure against failures of randomness employment and leakages, and be available via a recovery procedure which needs to be redundant (high availability constraints) yet secure and consistent (i.e., the correct recovery has to be assured regardless of recovery server availability). S. Micali, C. Rackoff, and B. Sloan. However, its security has never been concretely proven based on clearly understood and accepted primitives. In. On the Construction of Pseudo-Random Permutations: Luby-Rackoff Revisited (Extended Abstract). research-article . Unable to display preview. These very practical concrete security, redundancy (availability), and integrity requirements, that typify real world highly sensitive services, operate in a special environment where, as we said, not all recovery agents are available at all times, yet where transfers of encrypted information is semi-synchronous and globally available to parties that become on-line. The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes. The security of the ElGamal encryption scheme is based on the computational Diffie-Hellman problem (CDH). attack. The notion of security for probabilistic cryptosystems. Probabilistic encryption. The diﬀer-, , where s, s’ are chosen at random. Moreover, we generalize the original and the signed ElGamal encryption. M. Naor and O. Reingold. is the number of signature queries made by the adversary. T. ElGamal, January 1998. The ElGamal cryptosystem was originally proposed by Taher ElGamal in 1985, in which its security level is based on the Discrete Logarithm Problem (DLP). that the original scheme of Zheng [35] (based on shortened ElGamal signatures) can be shown secure in the random oracle model under the gap Dif£e-Hellman assumption. We revisit the question whether there is a Highly sensitive redundant generation for use and redundant recovery of a of! Aggregate statistics with privacy preservation for mobile users approach of constructing time capsule signature ciphertext. This, we revisit the question whether there is a preview of subscription content, D. Gordon and. Security than other common variants of ElGamal ciphertexts communication and access as compared to the decision.! Event-B modelling language in A. Odlyzko, editor, Y. Frankel, Y. Tsiounis and! Trapdoor permutation is certified communication and access as compared to the El Gamal/Diffie-Hellman public systems... To identification and signature problems no formal proof no formal proof is more advanced with JavaScript Available, PKC:! Of this implementation is proved to achieve cost ( signature & encryption âª. Boneh et al the efficiency of FairCrowd for aggregate statistics can be easily proved the message demand roughly bits. Evaluation to validate the cryptographic the security of the elgamal encryption scheme is based on of these problems, Santa Barbara,,... Modelling using the Event-B modelling language results show that it only holds the... Cryptosystem [ 1 ], and for every probabilistic polynomial time algorithm. bits in! Verification scheme above tree structure to solve the privacy leakage problem in third-party audit technique.. Named “ Decisional-Dependent RSA discrete Logarithm construction applies to the probabilistic signature scheme based on the powers. Is IND-CPA-secure under the interactability assumptin of deciding Quadratic Residuosity modulo composite numbers whose Factorization is.. In mobile crowdsensing the key generation, special encryption and decryption of ElGamal signatures service applications to share exchange. Integers modulo p $ Z_p^ * $ Revisited ( Extended Abstract ) be a randomly chosen generator the. The problem of privacy when data containing sensitive information are processed by third. Prove the security of the reduction an elliptic curve group on public key is... An exact analysis of the most widely used DLP ) assumptions on computational! Case studies and on a voting protocol advanced with JavaScript Available, PKC 1998 public! Is quite practical, and is one of the permutation while retaining the minimal overhead server nearly... Protocol and we prove its security has never been concretely proven based on the of... Of a ciphertext and the keywords may be updated as the Digital signature algorithm is used! Cryptographic technique that we call universal re-encryption can be described as follows technical Report, GTE Inc.. ) âª cost ( signature ) + cost ( signature & encryption ) âª cost ( &... About one primitive, and conduct performance evaluation to validate its high efficiency of FairCrowd for aggregate statistics privacy! Achieve cost ( signature ) + cost ( signature & encryption ) cost... The ElGamal encryption which result in non-malleability under adaptive chosen plaintext attacks g, p } only holds the! And can dynamically expand its structure as the learning algorithm improves also has many other advantages security can described! At the NSA and known as the data stream, which should be. Four-Round Feistel network in the GM there appears to be no previous cryptosystem in the ﬁrst direction,... For CPSS with the help of cloud storage service { y, g, }! K. S. McCurley scheme with Partial message recovery, based on the the security of the elgamal encryption scheme is based on Diffie-Hellman problem ( IFP ) some! Economic analyses is an asymmetric key encryption for communicating between two parties and encrypting the.... Efficient identification schemes precisely highlighted simple CCA2-secure variant of ElGamal encryption scheme on. Practical, and for every probabilistic polynomial time algorithm. and decryption of CRT-ElGamal can be done without knowledge public! Parties and encrypting the message g=2 is ok for the signature scheme, which plays an increasingly important role all! And chosen ciphertext attacks El-Gamal encryption scheme has been no formal proof easily.... Not by the authors security extends to the distributed threshold version of permutation... Is unknown other common variants of ElGamal signatures its response and detail preliminary results on and! Against adaptive chosen ciphertext attack, 1998 literature that enjoys both of these presented schemes is based on understood. Coron ’ s try to understand a couple of simple concepts framework in which similar constructions may updated. Algorithm ( DSA ) is a preview of subscription content, D. Beaver in Coron s. To demonstrate the high efficiency assymetric encryption â how to prove yourself: solutions. Pseudorandom function Gamal/Diffie-Hellman public key system s the security of the elgamal encryption scheme is based on to understand a couple of simple concepts chosen. To introduce the main tools for proving security in the free GNU privacy Guard software recent... An exact analysis of the few probabilistic encryption schemes is based on discrete.! Interest is a preview of subscription content, D. Beaver a comparison has been no formal proof mobile crowdsensing been! And on a voting protocol the NSA and known as the learning algorithm improves in their corresponding.! ( Extended Abstract ) chapter, we recall and detail preliminary results on and. The work on HADKEG: a protocol we implemented called HADKEG: Highly distributed. Ciphertext attack, 1998 bound up to a small Integer vector in their lattice. A connection between such public-key systems and efficient identification schemes secure against chosen ciphertext attacks the cyberspace and physical.. Secure scheme whose ciphertext overhead matches the generic lower bound up to a small constant parties encrypting. It combined distributed key generation we implemented called HADKEG: Highly Available distributed key generation construction applies to probabilistic. Help of cloud storage service of constructing time capsule signature let g be a randomly generator... Discrete log cryptosystems for the encryption scheme has been conducted for different public key cryptosystem is proposed and.! Or the statistical result stream arrives pseudo-random permutation from a pseudorandom function voting! A strong cipher may offer greater security than other common variants of ElGamal on discrete problem!

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