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A Method for Obtaining Digital Signatures and PublicKey Cryptosystems
 Communications of the ACM
, 1978
"... An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: 1. Couriers or other secure means are not needed to transmit keys, since a message can be enciphered usin ..."
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Cited by 3847 (28 self)
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An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: 1. Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key. 2. A message can be "signed" using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in "electronic mail" and "electronic funds transfer" systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two lar...
The number of permutation binomials over F4p+1 where p and 4p+1 are primes, Electron
 J. Combin
"... We give a characterization of permutation polynomials over a finite field based on their coefficients, similar to Hermite’s Criterion. Then, we use this result to obtain a formula for the total number of monic permutation binomials of degree less than 4p over F4p+1, wherep and 4p + 1 are primes, in ..."
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Cited by 7 (3 self)
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We give a characterization of permutation polynomials over a finite field based on their coefficients, similar to Hermite’s Criterion. Then, we use this result to obtain a formula for the total number of monic permutation binomials of degree less than 4p over F4p+1, wherep and 4p + 1 are primes, in terms of the numbers of three special types of permutation binomials. We also briefly discuss the case q =2p +1withp and q primes. 1
Enumerating Permutation Polynomials I: Permutations with NonMaximal Degree
, 2002
"... s can be found in the book of Lidl and Niederreiter [5]. Various applications of permutation polynomials to cryptography have been described. See for example [1,2]. Lidl and Mullen in [3,4] (see also [6]) describe a number of open problems regarding permutations polynomials: among these, the problem ..."
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Cited by 3 (2 self)
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s can be found in the book of Lidl and Niederreiter [5]. Various applications of permutation polynomials to cryptography have been described. See for example [1,2]. Lidl and Mullen in [3,4] (see also [6]) describe a number of open problems regarding permutations polynomials: among these, the problem of enumerating permutation polynomials by their degree. We denote by S s fx 2 F sx=xg the set of those elements of F q which are moved by s. Our first remark is that @f s #q#j if s=id: 2 T see this it is enough to note that the polynomial f s x#x has as roots all the elements of F q fixed by s, that is which are not in S s .TgyyggC e, if not identically zero, it has to have degree at least q#j . An immediate consequence is that all transpositions give rise to permutation polynomials of degree exactly q # 2. TC s fact was noticed by Wells in [7], where he also proved the following: heorem 1.1 (Wells [7]). If q > 3, the number of 3cycles permutations s of F q such that @f s #q#3
Review Article ENHANCES SECURITY REDUCES TIME: DIGITAL SIGNATURES
"... A DIGITAL SIGNATURE is a mathematical scheme for demonstrating the authenticity of a digital message or document. It provides authentication, non repudiation and integrity to the message. Digital signatures are commonly used for software distribution, financial transactions, and in other cases where ..."
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A DIGITAL SIGNATURE is a mathematical scheme for demonstrating the authenticity of a digital message or document. It provides authentication, non repudiation and integrity to the message. Digital signatures are commonly used for software distribution, financial transactions, and in other cases where it is important to detect forgery or tampering and they are also known as the “CRYPTOGRAPHIC SIGNATURES OR ELECTRONIC SIGNATURES”. With the development of Internet, digital signature becomes more and more important for the electronic commerce security because of its data integrity protecting and privacy. Anyone can verify this signature using the corresponding publicly revealed encryption key. Considered by the electronic signature industry as the most reliable way to sign of the three types of electronic signatures and the only standard signing solution available, digital signatures are a thoroughlytested and well established technology.
Enumerating permutation polynomials II: kcycles with minimal degree
"... We consider the function mkðqÞ that counts the number of cycle permutations of a finite field Fq of fixed length k such that their permutation polynomial has the smallest possible degree. We prove the upperbound mkðqÞpðk 1Þ!ðqðq 1ÞÞ=k for charðFqÞ4eðk3Þ=e and the lowerbound mkðqÞXjðkÞðqðq 1ÞÞ=k ..."
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We consider the function mkðqÞ that counts the number of cycle permutations of a finite field Fq of fixed length k such that their permutation polynomial has the smallest possible degree. We prove the upperbound mkðqÞpðk 1Þ!ðqðq 1ÞÞ=k for charðFqÞ4eðk3Þ=e and the lowerbound mkðqÞXjðkÞðqðq 1ÞÞ=k for q 1 ðmod kÞ: This is done by establishing a connection with the Fqsolutions of a system of equationsAk defined over Z: As example, we give complete formulas for mkðqÞ when k 4; 5 and partial formulas for k 6: Finally, we analyze the Galois structure of the algebraic set Ak: r 2003 Elsevier Inc. All rights reserved. 1.
Programming Techniques S.L. Graham, R.L. Rivest* Editors A Method for Obtaining Digital Signatures and Public
"... An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered usi ..."
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An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key. (2) A message can be &quot;signed &quot; using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in &quot;electronic mail &quot; and &quot;electronic funds transfer &quot; systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret prime numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d l(mod (p 1) * (q 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n. Key Words and Phrases: digital signatures, publickey cryptosystems, privacy, authentication, security, factorization, prime number, electronic mail, messagepassing, electronic funds transfer, cryptography.
Programming S.L. Graham, R.L. Rivest * Techniques Editors A Method for Obtaining Digital Signatures and
"... An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered usi ..."
Abstract
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An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key. (2) A message can be “signed ” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail ” and “electronic funds transfer ” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret prime numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d ≡ 1 (mod (p – 1) * (q – 1)). The security of the system rests in part on the difficulty of factoring the published divisor n.
NonLinearity and Affine Equivalence of Permutations
, 2014
"... In this paper we consider permutations on n symbols as bijections on Z/nZ. Treating permutations this way facilitates us with additional structures such as group, ring defined in the set Z/nZ. We explore some of the properties of permutations arising out of this treatment. We propose two properties ..."
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In this paper we consider permutations on n symbols as bijections on Z/nZ. Treating permutations this way facilitates us with additional structures such as group, ring defined in the set Z/nZ. We explore some of the properties of permutations arising out of this treatment. We propose two properties viz. affine equivalence and nonlinearity for permutations on the lines similar to there description given in the case of functions. We also establish some results which are quite similar to those given for Boolean functions. We also define Mode Transform of a permutation and investigate its relationship with nonlinearity. We propose an efficient algorithm using Mode transform for computing nonlinearity of a permutation and show that it is O(n2), as compared to O(n3) of the direct approach. At the end we discuss these properties in the context of cryptography.