A pseudo-random bit generator based on elliptic logarithms
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STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
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SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Finding a small root of a bivariate integer equation; factoring with high bits known
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Kleptography: using cryptography against cryptography
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
An elliptic curve backdoor algorithm for RSASSA
IH'06 Proceedings of the 8th international conference on Information hiding
Simple backdoors for RSA key generation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
The Twist-AUgmented technique for key exchange
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Stealing secrets with SSL/TLS and SSH – kleptographic attacks
CANS'06 Proceedings of the 5th international conference on Cryptology and Network Security
A space efficient backdoor in RSA and its applications
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Kleptography from standard assumptions and applications
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
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In the past, hiding asymmetric backdoors inside cryptosystems required a random oracle assumption (idealization) as "randomizers" of the hidden channels. The basic question left open is whether cryptography itself based on traditional hardness assumption(s) alone enables "internal randomized channels" that enable the embedding of an asymmetric backdoor inside another cryptosystem while retaining the security of the cryptosystem and the backdoor (two security proofs in one system). This question translates into the existence of kleptographic channels without the idealization of random oracle functions. We therefore address the basic problem of controlling the probability distribution over information (i.e., the kleptogram) that is hidden within the output of a cryptographic system. We settle this question by presenting an elliptic curve asymmetric backdoor construction that solves this problem. As an example, we apply the construction to produce a provably secure asymmetric backdoor in SSL. The construction is general and applies to many other kleptographic settings as well.