P. Smith. LUC Public-key Encryption. Dr. Dobb's Journal, 18(1):44{ 49, 90-92, January 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....large integers. After this breakthrough, other structures were proposed to produce analogues to RSA. So, Muller and Nobauer [54, 55] presented a cryptosystem using Dickson polynomials. This system was afterwards slightly modified and rephrased in terms of Lucas sequences by Smith and Lennon [70, 72]. More recently, Koyama, Maurer, Okamoto and Vanstone [41] exhibited new one way trapdoor functions similar to RSA on elliptic curves, the so called KMOV cryptosystem. Later, Demytko [20] also pointed out a new one way trapdoor function on elliptic curves to produce an analogue of RSA. There are ....

....(# p) where p is a prime that does not divide 2#. Then, U k#(p) 1 (P, 1) U 1 (P, 1) 1 (mod p) 2.7) V k#(p) 1 (P, 1) V 1 (P, 1) P (mod p) 2.8) Identity (2.8) enables to construct a RSA like cryptosystem based on Lucas sequences with parameters P , Q = 1 and # = P 4. 2.2. LUC [70, 72]. Each user chooses two large primes p and q, and publishes the product n = pq. Next, he chooses a public encryption key e that is relatively prime to (p 1) p 1) q 1) and (q 1) Finally, he computes the secret decryption key d according to 1 (mod #(n) 2.9) where #(n) ....

P. Smith, LUC public-key encryption, Dr. Dobb's Journal (1993), 44--49.

....the intended receiver of the message is assumed to know the key. When the cryptographic key used for encryption is the same as that to be used for decryption, cryptography is said to be symmetric or shared key (DES [81] IDEA [61] etc. otherwise it is asymmetric or public key (RSA [93] LUC [99], etc. In the sequel, we assume a basic familiarity with these techniques. Steganography [55] may also be used towards secure communications. It is the art of hiding a message inside a larger, intelligible one so that the spy cannot discern the presence of the hidden message from seeing the ....

P. Smith. LUC Public-key Encryption. Dr. Dobb's Journal, 18(1):44-- 49, 90--92, January 1993.

....another candidate trapdoor one way permutation based on the factoring problem. Notes : 1. The Dickson polynomials are also known as Chebyshev polynomials of the rst kind. 2. In 1993, the scheme of M uller and N obauer was re invented (with minor di erences) by P.J. Smith, who called it LUC (see [25] and [26] This cryptosystem is formulated in terms of Lucas sequences. Some variations of LUC were also developed as (non bijective) analogies to the ElGamal scheme. Daniel Bleichenbacher, Wieb Bosma and Arjen K. Lenstra (see [1] showed that because of the deep links between Lucas sequences ....

P.J. Smith, LUC Public-Key Encryption, Dr. Dobb's Journal, January 1993, pp. 44-49.

....the previous attack, we will show that a cryptanalyst will be able to recover all the secrets keys, and not only the ones encrypted with a small exponent. Last but not least, our attack is of very general nature. It applies on many public key cryptosystems, including RSA [24] Rabin [23, 30] LUC [27], KMOV [19] Demytko [8] ElGamal [12] and its analogues [28, 17] 3 pass system [10] knapsack scheme [25] etc. The basic idea of our attack relies on the possibility to get access to the bin of the recipient. In fact, if the cryptanalyst intercepts, transforms and re sends a ciphertext, ....

Smith, P. LUC public-key encryption. Dr. Dobb's Journal (Jan. 1993), 44--49.

....chosen large integers. After this breakthrough, other structures were proposed to produce analogues to RSA. So, Muller and Nobauer [54, 55] presented a cryptosystem using Dickson polynomials. This system was afterwards slightly modified and rephrased in terms of Lucas sequences by Smith and Lennon [70, 72]. More recently, Koyama, Maurer, Okamoto and Vanstone [41] exhibited new one way trapdoor functions similar to RSA on elliptic curves, the so called KMOV cryptosystem. Later, Demytko [20] also pointed out a new one way trapdoor function on elliptic curves to produce an analogue of RSA. There are ....

....prime that does not divide 2 Delta. Then, U k Psi(p) 1 (P; 1) j U 1 (P; 1) 1 (mod p) 2.7) V k Psi(p) 1 (P; 1) j V 1 (P; 1) P (mod p) 2.8) Identity (2.8) enables to construct a RSA like cryptosystem based on Lucas sequences with parameters P , Q = 1 and Delta = P 2 Gamma 4. 2.2. LUC [70, 72]. Each user chooses two large primes p and q, and publishes the product n = pq. Next, he chooses a public encryption key e that is relatively prime to (p Gamma 1) p 1) q Gamma 1) and (q 1) Finally, he computes the secret decryption key d according to ed j 1 (mod Psi(n) 2.9) where ....

P. Smith, LUC public-key encryption, Dr. Dobb's Journal (1993), 44--49.

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P. Smith. LUC Public-key Encryption. Dr. Dobb's Journal, 18(1):44{ 49, 90-92, January 1993.

No context found.

Smith, P. LUC public-key encryption. Dr. Dobb's Journal (Jan. 1993), 44--49.

No context found.

Peter Smith. LUC public-key encryption. Dr. Dobb's Journal, pp. 44--49, Jan. 1993.

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P. Smith. LUC public-key encryption. Dr. Dobb's Journal, pages 44-49, January 1993.

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Smith, P. LUC public-key encryption. Dr. Dobb's Journal (Jan. 1993), 44--49.

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