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Generalisation of RSA Scheme using fundamental groups and ZKIP
"... Abstract We address the problem of computation involved in RSA algorithm namely exponentiation under modulo arithmetic and various mathematical and timing attacks in RSA. The computation is made easy and quick by assigning elements from the fundamental group in algebraic topology. This can also be ..."
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Abstract We address the problem of computation involved in RSA algorithm namely exponentiation under modulo arithmetic and various mathematical and timing attacks in RSA. The computation is made easy and quick by assigning elements from the fundamental group in algebraic topology. This can also
How To Prove Yourself: Practical Solutions to Identification and Signature Problems
, 1987
"... In this paper we describe simple identification and signature schemes which enable any user to prove his identity and the authenticity of his messages to any other user without shared or public keys. The schemes are provably secure against any known or chosen message attack ff factoring is difficult ..."
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Cited by 1026 (1 self)
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is difficult, and typical implementations require only 1% to 4% of the number of modular multiplications required by the RSA scheme. Due to their simplicity, security and speed, these schemes are ideally suited for microprocessorbased devices such as smart cards, personal computers, and remote control system.q.
A semantically secure elliptic curve RSA scheme with small expansion factor
, 2002
"... We propose an elliptic curve scheme over the ring Z n which is efficient and semantically secure in the standard model, and it has expansion factor 2 (previous schemes with similar features present expansion factors greater or equal than 4). Demytko's RSA type scheme has been used as an underly ..."
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We propose an elliptic curve scheme over the ring Z n which is efficient and semantically secure in the standard model, and it has expansion factor 2 (previous schemes with similar features present expansion factors greater or equal than 4). Demytko's RSA type scheme has been used
2.2 Standard CRTRSA Scheme and Fault Cryptanalysis
"... Let n = pq denote the RSA modulus with two primes p and q, e the public key and d the corresponding private key, so that ed ≡ 1 (mod ϕ(n)), where the Euler Totient of n is ϕ(n) = (p − 1)(q − 1). Let f(x) denote the faulty value on a variable x if an error occurs during the computation of x, and l(x ..."
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Let n = pq denote the RSA modulus with two primes p and q, e the public key and d the corresponding private key, so that ed ≡ 1 (mod ϕ(n)), where the Euler Totient of n is ϕ(n) = (p − 1)(q − 1). Let f(x) denote the faulty value on a variable x if an error occurs during the computation of x, and l
The exact security of digital signatures  How to sign with RSA and Rabin
, 1996
"... We describe an RSAbased signing scheme called PSS which combines essentially optimal efficiency with attractive security properties. Signing takes one RSA decryption plus some hashing, ..."
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Cited by 387 (17 self)
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We describe an RSAbased signing scheme called PSS which combines essentially optimal efficiency with attractive security properties. Signing takes one RSA decryption plus some hashing,
Publickey cryptosystems based on composite degree residuosity classes
 IN ADVANCES IN CRYPTOLOGY — EUROCRYPT 1999
, 1999
"... This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to publickey cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes: a trapdoor permutation and two homomorphic probabilist ..."
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Cited by 1007 (4 self)
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probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.
Short Signatures without Random Oracles
, 2004
"... We describe a short signature scheme which is existentially unforgeable under a chosen message attack without using random oracles. The security of our scheme depends on a new complexity assumption we call the Strong Di#eHellman assumption. This assumption has similar properties to the Strong RS ..."
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Cited by 393 (11 self)
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RSA assumption, hence the name. Strong RSA was previously used to construct signature schemes without random oracles. However, signatures generated by our scheme are much shorter and simpler than signatures from schemes based on Strong RSA.
On the Importance of Checking Cryptographic Protocols for Faults
, 1997
"... We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous s ..."
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Cited by 405 (6 self)
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We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous
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