A new public key cryptosystem based on higher residues

Naccache, David; Stern, Jacques

doi:10.1145/288090.288106

Cited by 261 publications

(198 citation statements)

References 20 publications

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“…Finally we compare the efficiency of our scheme with general 2-party computation protocols. We also propose in an appendix another solution, much more simple and efficient but less general, based on the higher residue cryptosystem of Naccache and Stern [19].…”

Section: Our Resultsmentioning

confidence: 99%

Generation of Shared RSA Keys by Two Parties

Poupard

Stern

1998

Lecture Notes in Computer Science

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Abstract. At Crypto'97 Boneh and Franklin proposed a protocol to efficiently generate shared RSA keys. In the case of two parties, the drawback of their scheme is the need of an independent third party. Furthermore, the security is guaranteed only if the three players follow the protocol. In this paper, we propose a protocol that enables two parties to evaluate any algebraic expression, including an RSA modulus, along the same lines as in the Boneh-Franklin protocol. Our solution does not need the help of a third party and the only assumption we make is the existence of an oblivious transfer protocol. Furthermore, it remains robust even if one of the two players deviates from the protocol.

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Section: Our Resultsmentioning

confidence: 99%

Generation of Shared RSA Keys by Two Parties

Poupard

Stern

1998

Lecture Notes in Computer Science

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“…Various subgroup membership problems have been extensively studied in the literature, and examples include the Decision Diffie-Hellman problem [11], the quadratic residue problem [18], among others [28,31,33]. Our constructions however are more related to the problems described in [16,29].…”

Section: Abstract Group Structurementioning

confidence: 99%

“…The subgroup membership problem has appeared in many different forms in the literature [11,18,28,31,33,16,29]. The subgroup escape problem has not been studied before.…”

Section: Introductionmentioning

confidence: 99%

Spreading Alerts Quietly and the Subgroup Escape Problem

Aspnes

Diamadi

Gjøsteen

et al. 2005

Lecture Notes in Computer Science

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Abstract. We introduce a new cryptographic primitive called the blind coupon mechanism (BCM). In effect, the BCM is an authenticated bit commitment scheme, which is AND-homomorphic. It has not been known how to construct such commitments before. We show that the BCM has natural and important applications. In particular, we use it to construct a mechanism for transmitting alerts undetectably in a message-passing system of n nodes. Our algorithms allow an alert to quickly propagate to all nodes without its source or existence being detected by an adversary, who controls all message traffic. Our proofs of security are based on a new subgroup escape problem, which seems hard on certain groups with bilinear pairings and on elliptic curves over the ring Zn.

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“…-For any polynomial-time adversary and for any given z = f (x, y), it is computationally infeasible to get back the partial preimage x, -With some extra secret information, it is easy to get back the x. Not only ElGamal [7], Okamoto-Uchiyama [22], Naccache-Stern [20] and Paillier [23] primitives, but also McEliece primitive can be categorized in PTOWF. Therefore Pointcheval's generic conversion is also applicable to the McEliece PKC with the same proof in [24].…”

Section: Notationsmentioning

confidence: 99%

Semantically Secure McEliece Public-Key Cryptosystems -Conversions for McEliece PKC -

Kobara

Imai

2001

Public Key Cryptography

129

105

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Abstract. Almost all of the current public-key cryptosystems (PKCs) are based on number theory, such as the integer factoring problem and the discrete logarithm problem (which will be solved in polynomial-time after the emergence of quantum computers). While the McEliece PKC is based on another theory, i.e. coding theory, it is vulnerable against several practical attacks. In this paper, we carefully review currently known attacks to the McEliece PKC, and then point out that, without any decryption oracles or any partial knowledge on the plaintext of the challenge ciphertext, no polynomial-time algorithm is known for inverting the McEliece PKC whose parameters are carefully chosen. Under the assumption that this inverting problem is hard, we propose slightly modified versions of McEliece PKC that can be proven, in the random oracle model, to be semantically secure against adaptive chosen-ciphertext attacks. Our conversions can achieve the reduction of the redundant data down to 1/3 ∼ 1/4 compared with the generic conversions for practical parameters.

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A new public key cryptosystem based on higher residues

Cited by 261 publications

References 20 publications

Generation of Shared RSA Keys by Two Parties

Generation of Shared RSA Keys by Two Parties

Spreading Alerts Quietly and the Subgroup Escape Problem

Semantically Secure McEliece Public-Key Cryptosystems -Conversions for McEliece PKC -

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