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Efficient generation of shared RSA keys
 Advances in Cryptology  CRYPTO 97
, 1997
"... We describe efficient techniques for a number of parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known. None of the parties know the factorization of N. In addition a public encryption exponent is publicly known and each party holds a share of the ..."
Abstract

Cited by 151 (5 self)
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We describe efficient techniques for a number of parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known. None of the parties know the factorization of N. In addition a public encryption exponent is publicly known and each party holds a share of the private exponent that enables threshold decryption. Our protocols are efficient in computation and communication. All results are presented in the honest but curious settings (passive adversary).
Two Party RSA Key Generation
 In Crypto ’99, LNCS 1666
, 1999
"... . We present a protocol for two parties to generate an RSA key in a distributed manner. At the end of the protocol the public key: a modulus N = PQ, and an encryption exponent e are known to both parties. Individually, neither party obtains information about the decryption key d and the prime fa ..."
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Cited by 34 (0 self)
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. We present a protocol for two parties to generate an RSA key in a distributed manner. At the end of the protocol the public key: a modulus N = PQ, and an encryption exponent e are known to both parties. Individually, neither party obtains information about the decryption key d and the prime factors of N : P and Q. However, d is shared among the parties so that threshold decryption is possible. 1 Introduction We show how two parties can jointly generate RSA public and private keys. Following the execution of our protocol each party learns the public key: N = PQ and e, but does not know the factorization of N or the decryption exponent d. The exponent d is shared among the two players in such a way that joint decryption of ciphertexts is possible. Generation of RSA keys in a private, distributed manner figures prominently in several cryptographic protocols. An example is threshold cryptography, see [12] for a survey. In a threshold RSA signature scheme there are k parties who ...
EULER’S CONSTANT: EULER’S WORK AND MODERN DEVELOPMENTS
, 2013
"... Abstract. This paper has two parts. The first part surveys Euler’s work on the constant γ =0.57721 ·· · bearing his name, together with some of his related work on the gamma function, values of the zeta function, and divergent series. The second part describes various mathematical developments invol ..."
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Cited by 12 (1 self)
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Abstract. This paper has two parts. The first part surveys Euler’s work on the constant γ =0.57721 ·· · bearing his name, together with some of his related work on the gamma function, values of the zeta function, and divergent series. The second part describes various mathematical developments involving Euler’s constant, as well as another constant, the Euler–Gompertz constant. These developments include connections with arithmetic functions and the Riemann hypothesis, and with sieve methods, random permutations, and random matrix products. It also includes recent results on Diophantine approximation and transcendence related to Euler’s constant. Contents
Efficient rsa key generation and threshold paillier in the twoparty setting. Cryptology ePrint Archive
, 2011
"... The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first nongeneric fully simulatable protocol for distributively generating an RSA composite with ..."
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Cited by 8 (2 self)
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The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first nongeneric fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is complete Paillier [Pai99] threshold encryption scheme in the twoparty setting with security against malicious behavior. Furthermore, we describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation is comprised of the following: (i) a distributed protocol for generation of an RSA composite, and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite as public key and is comprised of: (i) a distributed generation of the corresponding secretkey shares and, (ii) a distributed decryption protocol for decrypting according to Paillier. Keywords:
Efficient Generation of Shared RSA keys (Extended Abstract)
 In Kaliski [103
"... We describe efficient techniques for three (or more) parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known. None of the parties know the factorization of N . In addition a public encryption exponent is publicly known and each party holds a share o ..."
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Cited by 7 (1 self)
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We describe efficient techniques for three (or more) parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known. None of the parties know the factorization of N . In addition a public encryption exponent is publicly known and each party holds a share of the private exponent that enables threshold decryption. Our protocols are efficient in computation and communication.
Sets of integers and quasiintegers with pairwise common divisor
 Acta Arith
, 1996
"... u ∈ N: u, s−1 ..."
Nicolaas Govert de Bruijn, the enchanter of friable integers
 Indagationes Math
"... ar ..."
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Experimental Performance of Shared RSA Modulus Generation
 In proceedings of SODA '99
, 1998
"... y ..."
Maximal Sets of Numbers Not Containing K+1 Pairwise Coprime Integers
"... For positive integers k; n let f(n; k) be the maximal cardinality of subsets of integers in the interval ! 1; n ? , which don't have k + 1 pairwise coprimes. The set E (n; k) of integers in ! 1; n ? , which are divisible by one of the first k primes, certainly does not have k + 1 pairwise copr ..."
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Cited by 1 (0 self)
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For positive integers k; n let f(n; k) be the maximal cardinality of subsets of integers in the interval ! 1; n ? , which don't have k + 1 pairwise coprimes. The set E (n; k) of integers in ! 1; n ? , which are divisible by one of the first k primes, certainly does not have k + 1 pairwise coprimes. Whereas we disproved in [1] an old conjecture of Erdős ([4], [5], [6], [7]) by showing that the equality (1) f(n; k) = jE (n; k)j does not always hold, we prove here that (1) holds for every k and all relative to k sufficiently large n .