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On optimal heuristic randomized semidecision procedures, with applications to proof complexity and cryptography
, 2010
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A feebly secure trapdoor function
"... In 1992, A. Hiltgen [1] provided the first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as circuit complexity over circuits with arbitrary binary gates) ..."
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Cited by 6 (4 self)
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In 1992, A. Hiltgen [1] provided the first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as circuit complexity over circuits with arbitrary binary gates) is amplified by a constant factor only (with the factor approaching 2). In traditional cryptography, oneway functions are the basic primitive of privatekey and digital signature schemes, while publickey cryptosystems are constructed with trapdoor functions. We continue Hiltgen’s work by providing an example of a feebly trapdoor function where the adversary is guaranteed to spend more time than every honest participant by a constant factor of 25/22.
New Combinatorial Complete OneWay Functions
 in Proc. 25th Sympos. on Theoretical Aspects of Computer Science
, 2008
"... In 2003, Leonid A. Levin presented the idea of a combinatorial complete oneway function and a sketch of the proof that Tiling represents such a function. In this paper, we present two new oneway functions based on semiThue string rewriting systems and a version of the Post Correspondence Problem ..."
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Cited by 4 (4 self)
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In 2003, Leonid A. Levin presented the idea of a combinatorial complete oneway function and a sketch of the proof that Tiling represents such a function. In this paper, we present two new oneway functions based on semiThue string rewriting systems and a version of the Post Correspondence Problem and prove their completeness. Besides, we present an alternative proof of Levin’s result. We also discuss the properties a combinatorial problem should have in order to hold a complete oneway function. 1
Feebly secure cryptographic primitives
, 2011
"... In 1992, A. Hiltgen [9] provided first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as the circuit complexity over circuits with arbitrary binary gates) ..."
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Cited by 2 (2 self)
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In 1992, A. Hiltgen [9] provided first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as the circuit complexity over circuits with arbitrary binary gates) is amplified only by a constant factor (in Hiltgen’s works, the factor approaches 2). In traditional cryptography, oneway functions are the basic primitive of privatekey schemes, while publickey schemes are constructed using trapdoor functions. We continue Hiltgen’s work by providing examples of feebly secure trapdoor functions where the adversary is guaranteed to spend more time than honest participants (also by a constant factor). We give both a (simpler) linear and a (better) nonlinear construction.
A feebly trapdoor function
, 2008
"... In 1992, A. Hiltgen [Hil92] provided the first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as circuit complexity over circuits with arbitrary binary ga ..."
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Cited by 1 (1 self)
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In 1992, A. Hiltgen [Hil92] provided the first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as circuit complexity over circuits with arbitrary binary gates) is amplified only by a constant factor (in Hiltgen’s works, the factor approaches 2). In traditional cryptography, oneway functions are the basic primitive of privatekey and digital signature schemes, while publickey cryptosystems are constructed with trapdoor functions. We continue Hiltgen’s work by providing an example of a feebly trapdoor function where the adversary is guaranteed to spend more time than the honest participants (also by a constant factor).
www.stacsconf.org NEW COMBINATORIAL COMPLETE ONEWAY FUNCTIONS
, 802
"... Abstract. In 2003, Leonid A. Levin presented the idea of a combinatorial complete oneway function and a sketch of the proof that Tiling represents such a function. In this paper, we present two new oneway functions based on semiThue string rewriting systems and a version of the Post Correspondenc ..."
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Abstract. In 2003, Leonid A. Levin presented the idea of a combinatorial complete oneway function and a sketch of the proof that Tiling represents such a function. In this paper, we present two new oneway functions based on semiThue string rewriting systems and a version of the Post Correspondence Problem and prove their completeness. Besides, we present an alternative proof of Levin’s result. We also discuss the properties a combinatorial problem should have in order to hold a complete oneway function. 1.
Algebraic cryptography: new constructions and their security against provable break
, 2008
"... Very few known cryptographic primitives are based on noncommutative algebra. Each new scheme is of substantial interest, because noncommutative constructions are secure against many standard cryptographic attacks. On the other hand, cryptography does not provide security proofs that would allow to b ..."
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Very few known cryptographic primitives are based on noncommutative algebra. Each new scheme is of substantial interest, because noncommutative constructions are secure against many standard cryptographic attacks. On the other hand, cryptography does not provide security proofs that would allow to base the security of a cryptographic primitive on structural complexity assumptions. Thus, it is important to investigate weaker notions of security. In this paper we introduce new constructions of cryptographic primitives based on group invariants and o er new ways to strengthen them for practical use. Besides, we introduce the notion of provable break which is a weaker version of the regular cryptographic break. In this version, an adversary should have a proof that he has correctly decyphered the message. We prove that cryptosystems based on matrix groups invariants and a version of the AnshelAnshelGoldfeld key agreement protocol for modular groups are secure against provable break unless NP = RP.
On Complete OneWay Functions
, 2009
"... Complete constructions play an important role in theoretical computer science. However, in cryptography complete constructions have so far been either absent or purely theoretical. In 2003, L.A. Levin presented the idea of a combinatorial complete oneway function. In this paper, we present two new ..."
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Complete constructions play an important role in theoretical computer science. However, in cryptography complete constructions have so far been either absent or purely theoretical. In 2003, L.A. Levin presented the idea of a combinatorial complete oneway function. In this paper, we present two new oneway functions based on semiThue string rewriting systems and a version of the Post correspondence problem. We also present the properties of a combinatorial problem that allow a complete oneway function to be based on this problem. The paper also gives an alternative proof of Levin’s result.
www.stacsconf.org ON OPTIMAL HEURISTIC RANDOMIZED SEMIDECISION PROCEDURES, WITH APPLICATION TO PROOF COMPLEXITY
"... Abstract. The existence of a (p)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal 1 on all propos ..."
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Abstract. The existence of a (p)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal 1 on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms do exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false “theorems ” (according to any polynomialtime samplable distribution on nontautologies) and err with bounded probability on other inputs. Our result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems. 1.
0Provably Secure Cryptographic Constructions
"... 1.1 Cryptography: treading uncertain paths Modern cryptography has virtually no provably secure constructions. Starting from the first Diffie–Hellman key agreement protocol (Diffie & Hellman, 1976) and the first public key cryptosystemRSA (Rivest et al., 1978), not a single public key cryptograp ..."
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1.1 Cryptography: treading uncertain paths Modern cryptography has virtually no provably secure constructions. Starting from the first Diffie–Hellman key agreement protocol (Diffie & Hellman, 1976) and the first public key cryptosystemRSA (Rivest et al., 1978), not a single public key cryptographic protocol has been