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Trapdooring Discrete Logarithms on Elliptic Curves over Rings
, 2000
"... This paper introduces three new probabilistic encryption schemes using elliptic curves over rings. The cryptosystems are based on three specific trapdoor mechanisms allowing the recipient to recover discrete logarithms on di#erent types of curves. The first scheme is an embodiment of Naccache an ..."
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Cited by 17 (0 self)
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This paper introduces three new probabilistic encryption schemes using elliptic curves over rings. The cryptosystems are based on three specific trapdoor mechanisms allowing the recipient to recover discrete logarithms on di#erent types of curves. The first scheme is an embodiment of Naccache and Stern's cryptosystem and realizes a discrete log encryption as originally wanted in [23] by Vanstone and Zuccherato.
Elliptic Curve Paillier Schemes
, 2001
"... . This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schemes ar ..."
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Cited by 16 (0 self)
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. This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schemes are not secure. A more natural generalisation of Paillier's scheme to elliptic curves is given.
On the relations between noninteractive key distribution, identitybased encryption and trapdoor discrete log groups. Cryptology ePrint Archive, Report 2007/453
, 2007
"... Abstract. This paper investigates the relationships between identitybased noninteractive key distribution (IDNIKD) and identitybased encryption (IBE). It provides a new security model for IDNIKD, and a generic construction that converts a secure IDNIKD scheme into a secure IBE scheme. This con ..."
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Cited by 10 (2 self)
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Abstract. This paper investigates the relationships between identitybased noninteractive key distribution (IDNIKD) and identitybased encryption (IBE). It provides a new security model for IDNIKD, and a generic construction that converts a secure IDNIKD scheme into a secure IBE scheme. This conversion is used to explain the relationship between the IDNIKD scheme of Sakai, Ohgishi and Kasahara and the IBE scheme of Boneh and Franklin. The paper then explores the construction of IDNIKD and IBE schemes from general trapdoor discrete log groups. Two different concrete instantiations for such groups provide new, provably secure IDNIKD and IBE schemes. These schemes are suited to applications in which the Trusted Authority is computationally wellresourced, but clients performing encryption/decryption are highly constrained. Keywords: Identitybased encryption; identitybased noninteractive key distribution; trapdoor discrete logs. 1
Breaking RSA May Be As Difficult As Factoring
, 2005
"... If factoring is hard, then straight line programs cannot efficiently solve the low public exponent RSA problem. More precisely, no efficient algorithm can take an RSA public key as input and then output a straight line program that efficiently solves the low public exponent RSA problem for the given ..."
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Cited by 2 (0 self)
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If factoring is hard, then straight line programs cannot efficiently solve the low public exponent RSA problem. More precisely, no efficient algorithm can take an RSA public key as input and then output a straight line program that efficiently solves the low public exponent RSA problem for the given public key — unless factoring is easy. More generally, it suffices that the public exponent has a small factor. Of course, other kinds of algorithms may well be able to solve the RSA problem. 1
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"... On the relations between noninteractive key distribution, identitybased encryption and trapdoor discrete log groups ..."
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On the relations between noninteractive key distribution, identitybased encryption and trapdoor discrete log groups