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The Multivariate Probabilistic Encryption Scheme MQQENC
"... Abstract. We propose a new multivariate probabilistic encryption scheme with decryption errors MQQENC that belongs to the family of MQQbased public key schemes. Similarly to MQQSIG, the trapdoor is constructed using quasigroup string transformations with multivariate quadratic quasigroups, and a ..."
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Abstract. We propose a new multivariate probabilistic encryption scheme with decryption errors MQQENC that belongs to the family of MQQbased public key schemes. Similarly to MQQSIG, the trapdoor is constructed using quasigroup string transformations with multivariate quadratic quasigroups, and a
Publickey cryptosystems based on composite degree residuosity classes
 IN ADVANCES IN CRYPTOLOGY — EUROCRYPT 1999
, 1999
"... This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to publickey cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes: a trapdoor permutation and two homomorphic probabilist ..."
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Cited by 981 (4 self)
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probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.
Optimal Asymmetric Encryption
, 1994
"... Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string z of length slightly less than k bits can be encrypted as where r= is a simple probabilistic encoding of z depending on the hash function; and (ii) the scheme ca ..."
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Cited by 271 (14 self)
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Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string z of length slightly less than k bits can be encrypted as where r= is a simple probabilistic encoding of z depending on the hash function; and (ii) the scheme
On the (im)possibility of obfuscating programs
 Lecture Notes in Computer Science
, 2001
"... Informally, an obfuscator O is an (efficient, probabilistic) “compiler ” that takes as input a program (or circuit) P and produces a new program O(P) that has the same functionality as P yet is “unintelligible ” in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic an ..."
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Cited by 341 (24 self)
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approximately preserve the functionality, and (c) only need to work for very restricted models of computation (TC 0). We also rule out several potential applications of obfuscators, by constructing “unobfuscatable” signature schemes, encryption schemes, and pseudorandom function families.
Optimal Asymmetric Encryption – How to Encrypt with RSA
, 1995
"... Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme ..."
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Cited by 223 (21 self)
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Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii
A generalisation, a simplification and some applications of Paillier's probabilistic publickey system
 LNCS
, 2001
"... We propose a generalisation of Paillier’s probabilistic public key system, in which the expansion factor is reduced and which allows to adjust the block length of the scheme even after the public key has been fixed, without loosing the homomorphic property.We show that the generalisation is as secu ..."
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Cited by 218 (2 self)
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We propose a generalisation of Paillier’s probabilistic public key system, in which the expansion factor is reduced and which allows to adjust the block length of the scheme even after the public key has been fixed, without loosing the homomorphic property.We show that the generalisation
Evaluating 2dnf formulas on ciphertexts
 In proceedings of TCC ’05, LNCS series
, 2005
"... Abstract. Let ψ be a 2DNF formula on boolean variables x1,..., xn ∈ {0, 1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x1,..., xn. In other words, given the encryption of the bits x1,..., xn, anyone can create th ..."
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Cited by 227 (7 self)
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Abstract. Let ψ be a 2DNF formula on boolean variables x1,..., xn ∈ {0, 1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x1,..., xn. In other words, given the encryption of the bits x1,..., xn, anyone can create
Probabilistic Multivariate Cryptography
"... In public key schemes based on multivariate cryptography, the public key is a finite set of m (generally quadratic) polynomial equations and the private key is a trapdoor allowing the owner of the private key to invert the public key. In existing schemes, a signature or an answer to an authenticati ..."
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Cited by 1 (0 self)
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In public key schemes based on multivariate cryptography, the public key is a finite set of m (generally quadratic) polynomial equations and the private key is a trapdoor allowing the owner of the private key to invert the public key. In existing schemes, a signature or an answer
A new publickey cryptosystem as secure as factoring
 In Eurocrypt '98, LNCS 1403
, 1998
"... Abstract. This paper proposes a novel publickey cryptosystem, which is practical, provably secure and has some other interesting properties as follows: 1. Its trapdoor technique is essentially different from any other previous schemes including RSARabin and DiffieHellman. 2. It is a probabilistic ..."
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Cited by 204 (7 self)
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probabilistic encryption scheme. 3. It can be proven to be as secure as the intractability of factoring n = p 2 q (in the sense of the security of the whole plaintext) against passive adversaries. 4. It is semantically secure under the psubgroup assumption, which is comparable to the quadratic residue
Characterization of Security Notions for Probabilistic PrivateKey Encryption
 JOURNAL OF CRYPTOLOGY
, 2006
"... The development of precise definitions of security for encryption, as well as a detailed understanding of their relationships, has been a major area of research in modern cryptography. Here, we focus on the case of privatekey encryption. Extending security notions from the publickey setting, we ..."
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Cited by 67 (9 self)
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the definitions are equivalent, or whether they are incomparable. Second, we partition these notions of security into two classes (computational or informationtheoretic) depending on whether oneway functions are necessary in order for encryption schemes satisfying the definition to exist.
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