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Design and Analysis of Practical PublicKey Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack
 SIAM Journal on Computing
, 2001
"... A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first publickey encryption sc ..."
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Cited by 189 (11 self)
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A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first publickey encryption schemes in the literature that are simultaneously practical and provably secure.
Signature Schemes Based on the Strong RSA Assumption
 ACM TRANSACTIONS ON INFORMATION AND SYSTEM SECURITY
, 1998
"... We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the socalled Strong RSA Assumption. Moreove ..."
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Cited by 150 (8 self)
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We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the socalled Strong RSA Assumption. Moreover, a hash function can be incorporated into the scheme in such a way that it is also secure in the random oracle model under the standard RSA Assumption.
Largest known twin primes and Sophie Germain primes
 Math. Comp
, 1999
"... Abstract. The numbers 242206083 · 2 38880 ± 1 are twin primes. The number ..."
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Cited by 4 (0 self)
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Abstract. The numbers 242206083 · 2 38880 ± 1 are twin primes. The number
Prime specialization in genus 0
 Trans. Amer. Math. Soc
"... Abstract. For a prime polynomial f(T) ∈ Z[T], a classical conjecture predicts how often f has prime values. For a finite field κ and a prime polynomial f(T) ∈ κ[u][T], the natural analogue of this conjecture (a prediction for how often f takes prime values on κ[u]) is not generally true when f(T)i ..."
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Cited by 4 (2 self)
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Abstract. For a prime polynomial f(T) ∈ Z[T], a classical conjecture predicts how often f has prime values. For a finite field κ and a prime polynomial f(T) ∈ κ[u][T], the natural analogue of this conjecture (a prediction for how often f takes prime values on κ[u]) is not generally true when f(T)isapolynomial in T p (p the characteristic of κ). The explanation rests on a new global obstruction which can be measured by an appropriate average of the nonzero Möbius values µ(f(g)) as g varies. We prove the surprising fact that this “Möbius average, ” which can be defined without reference to any conjectures, has a periodic behavior governed by the geometry of the plane curve f =0. The periodic Möbius average behavior implies in specific examples that a polynomial in κ[u][T] does not take prime values as often as analogies with Z[T] suggest, and it leads to a modified conjecture for how often prime values occur. 1.
A Generalization Of A Conjecture Of Hardy And Littlewood To Algebraic Number Fields
 Rocky Mountain J. Math
, 1998
"... We generalize conjectures of Hardy and Littlewood concerning the density of twin primes and ktuples of primes to arbitrary algebraic number fields. In one of their great Partitio Numerorum papers [7], Hardy and Littlewood advance a number of conjectures involving the density of pairs and ktuples ..."
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Cited by 1 (0 self)
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We generalize conjectures of Hardy and Littlewood concerning the density of twin primes and ktuples of primes to arbitrary algebraic number fields. In one of their great Partitio Numerorum papers [7], Hardy and Littlewood advance a number of conjectures involving the density of pairs and ktuples of primes separated by fixed gaps. For example, if d is even, we define P d (x) = {0 < n < x : n, n + d are both prime}. They conjecture both that lim x## P d (x) P 2 (x) = # odd pd p  1 p  2 and that P 2 (x) is asymptotic to 2 # p>2 # 1  1 (p  1) 2 # # x 2 dy (log y) 2 . We will refer to the first equation as the "relative conjecture" and the second as the "absolute conjecture." There has been much numerical verification of these conjectures, and many attempts at proofs. Balog [1] proves a result that implies that the conjectures are true "on average," where the average is taken over the possible shapes of the ktuples. Golubev [6] compares these conjectures with provable analogous limit results for patterns of numbers prime to n. Turan [18] relates such theorems to zeroes of the #function, using the large sieve rather than Hardy and Littlewood's circle method. There are also many generalizations to specific fields. Most of those generalizations use "Conjecture H" of Sierpinski and Schinzel [14,15]. For example, Sierpinski [17] shows that Conjecture H implies the existence of infinitely many prime Gaussian integers di#ering by 2. Bateman and Horn [2,3] quote a quantitative form of Conjecture H which allows them to estimate the density of rational twin primes. Shanks [16] numerically verifies that the density of prime pairs of the form a + i, a + 2 + i in the Gaussian integers matches that of the quantitative form of Conjecture H. Rieger ...
with the BrezingWeng Method
, 2008
"... Abstract. The BrezingWeng method is a general framework to generate families of pairingfriendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endo ..."
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Abstract. The BrezingWeng method is a general framework to generate families of pairingfriendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endomorphism rings with small class number. Keywords: Pairingfriendly curve generation, BrezingWeng method. 1
LOWER BOUND FOR THE REMAINDER IN THE PRIMEPAIR CONJECTURE
, 806
"... Abstract. Taking r> 0 let π2r(x) denote the number of prime pairs (p, p + 2r) with p ≤ x. The primepair conjecture of Hardy and Littlewood (1923) asserts that π2r(x) ∼ 2C2r li2(x) with an explicit constant C2r> 0. A heuristic argument indicates that the remainder e2r(x) in this approximation canno ..."
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Abstract. Taking r> 0 let π2r(x) denote the number of prime pairs (p, p + 2r) with p ≤ x. The primepair conjecture of Hardy and Littlewood (1923) asserts that π2r(x) ∼ 2C2r li2(x) with an explicit constant C2r> 0. A heuristic argument indicates that the remainder e2r(x) in this approximation cannot be of lower order than x β, where β is the supremum of the real parts of zeta’s zeros. The argument also suggests an approximation for π2r(x) similar to one of Riemann for π(x). 1.
MEAN VALUE ONE OF PRIMEPAIR CONSTANTS
, 806
"... Abstract. For k> 1, r = 0 and large x, let πk 2r (x) denote the number of prime pairs (p, pk +2r) with p ≤ x. By the Bateman–Horn conjecture the function πk 2r(x) should be asymptotic to (2/k)Ck 2rli2(x), with certain specific constants Ck 2r. Heuristic arguments lead to the conjecture that these c ..."
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Abstract. For k> 1, r = 0 and large x, let πk 2r (x) denote the number of prime pairs (p, pk +2r) with p ≤ x. By the Bateman–Horn conjecture the function πk 2r(x) should be asymptotic to (2/k)Ck 2rli2(x), with certain specific constants Ck 2r. Heuristic arguments lead to the conjecture that these constants have mean value one, just like the Hardy–Littlewood constants C2r for prime pairs (p, p + 2r). The conjecture is supported by extensive numerical work. 1.
More Discriminants with the BrezingWeng Method
"... Abstract. The BrezingWeng method is a general framework to generate families of pairingfriendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endo ..."
Abstract
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Abstract. The BrezingWeng method is a general framework to generate families of pairingfriendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endomorphism rings with small class number. Keywords: Pairingfriendly curve generation, BrezingWeng method. 1