PeerJ Computer Science Preprints: Cryptographyhttps://peerj.com/preprints/index.atom?journal=cs&subject=9400Cryptography articles published in PeerJ Computer Science Preprints4, 8, 32, 64 bit Substitution Box generation using Irreducible or Reducible Polynomials over Galois Field GF(pq)https://peerj.com/preprints/33002017-09-292017-09-29Sankhanil DeyRanjan Ghosh
Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-Box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(28) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(pq). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log2q+1 bit BFs. So generation of log2q+1 bit S-Boxes is possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (pq ), where q = p-1.
Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-Box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(28) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(pq). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log2q+1 bit BFs. So generation of log2q+1 bit S-Boxes is possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (pq ), where q = p-1.Crypto-Archaeology: unearthing design methodology of DES s-boxeshttps://peerj.com/preprints/32852017-09-262017-09-26Sankhanil DeyRanjan Ghosh
US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.
US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.Multiplication and Division over Extended Galois Field GF(p^q): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(p^q).https://peerj.com/preprints/32592017-09-172017-09-17Sankhanil DeyRanjan Ghosh
Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both multiplication and division over Galois fields have been demonstrated to generate all monic IPs over extended Galois Field GF(p^q) for large value of both p and q. A little more efficient Algorithm entitled Multiplication Algorithm and more too Division Algorithm have been illustrated in this Paper with Algorithms to find all Monic IPs over extended Galois Field GF(p^q) for large value of both p and q. Time Complexity Analysis of three algorithms with comparison to Rabin’s Algorithms has also been exonerated in this Research Article.
Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both multiplication and division over Galois fields have been demonstrated to generate all monic IPs over extended Galois Field GF(p^q) for large value of both p and q. A little more efficient Algorithm entitled Multiplication Algorithm and more too Division Algorithm have been illustrated in this Paper with Algorithms to find all Monic IPs over extended Galois Field GF(p^q) for large value of both p and q. Time Complexity Analysis of three algorithms with comparison to Rabin’s Algorithms has also been exonerated in this Research Article.Multiplication over Extended Galois Field: A New Approach to Find Monic Irreducible Polynomials over Galois Field GF(p^q).https://peerj.com/preprints/32582017-09-172017-09-17Sankhanil DeyRanjan Ghosh
Searching for Monic Irreducible Polynomials (IPs) over extended Galois Field GF(p^q) for large value of prime moduli p and extension to Galois Field q is a well needed solution in the field of Cryptography. In this paper a new algorithm to obtain Monic IPs over extended Galois Fields GF(p^q) for large value of p and q has been introduced. The algorithm has been based on Multiplication algorithm over Galois Field GF(p^q).Time complexity analysis of the said algorithm has also been executed that ensures the algorithm to be less time consuming.
Searching for Monic Irreducible Polynomials (IPs) over extended Galois Field GF(p^q) for large value of prime moduli p and extension to Galois Field q is a well needed solution in the field of Cryptography. In this paper a new algorithm to obtain Monic IPs over extended Galois Fields GF(p^q) for large value of p and q has been introduced. The algorithm has been based on Multiplication algorithm over Galois Field GF(p^q).Time complexity analysis of the said algorithm has also been executed that ensures the algorithm to be less time consuming.Linear Approximation Analysis: an improved technique for linear cryptanalysis of 4-bit Bijective Crypto S-Boxeshttps://peerj.com/preprints/32492017-09-132017-09-13Sankhanil DeyRanjan Ghosh
4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective S-Boxes. Count of existence of all 4-bit Linear Relations, for all of 16 input and output 4-bit bit patterns of 4-bit Bijective S-Boxes said as S-Boxes has been reported in Linear Cryptanalysis of 4-bit S-Boxes. In this paper a brief review of this cryptanalytic method for 4-bit S-Boxes has been introduced in a very lucid and conceptual manner. A new Analysis to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing Linear Relations or Approximations in the contrary to count the number existence among all 16 4-bit input and output bit patterns for all possible linear approximations.
4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective S-Boxes. Count of existence of all 4-bit Linear Relations, for all of 16 input and output 4-bit bit patterns of 4-bit Bijective S-Boxes said as S-Boxes has been reported in Linear Cryptanalysis of 4-bit S-Boxes. In this paper a brief review of this cryptanalytic method for 4-bit S-Boxes has been introduced in a very lucid and conceptual manner. A new Analysis to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing Linear Relations or Approximations in the contrary to count the number existence among all 16 4-bit input and output bit patterns for all possible linear approximations.Extended SAC: A review and new algorithms of differential cryptanalysis of 4-bit s-boxes and strict avalanche criterion of BFs and 4-bit s-boxes again with a new extension to HO-SAC criterionhttps://peerj.com/preprints/32022017-09-122017-09-12Sankhanil DeyRanjan Ghosh
Bitwise-Xor of two 4 bit binary numbers or 4-bit bit patterns entitled 4-bit differences carries information in Cryptography. The Method to Analyze Cryptographic cipher algorithms or 4-bit substitution boxes with 4-bit differences is known as Differential Cryptanalysis. In this paper a brief review of Differential Cryptanalysis of 4-bit bijective Crypto S-Boxes and a new algorithm to analyze them using 4-bit Boolean Functions (BFs) have been introduced. A brief review of Strict Avalanche Criterion (SAC) of 4-bit bijective Crypto S-Boxes and 4-bit BFs and two new algorithms of both the aforesaid criterions have been introduced in this paper. A New algorithm entitled extended Strict Avalanche Criterion (An Extension to Higher Order SAC or HO-SAC) has also been introduced. A new Analysis of Similarity of extended HO-SAC and Differential Cryptanalysis has also been elaborated in this paper.
Bitwise-Xor of two 4 bit binary numbers or 4-bit bit patterns entitled 4-bit differences carries information in Cryptography. The Method to Analyze Cryptographic cipher algorithms or 4-bit substitution boxes with 4-bit differences is known as Differential Cryptanalysis. In this paper a brief review of Differential Cryptanalysis of 4-bit bijective Crypto S-Boxes and a new algorithm to analyze them using 4-bit Boolean Functions (BFs) have been introduced. A brief review of Strict Avalanche Criterion (SAC) of 4-bit bijective Crypto S-Boxes and 4-bit BFs and two new algorithms of both the aforesaid criterions have been introduced in this paper. A New algorithm entitled extended Strict Avalanche Criterion (An Extension to Higher Order SAC or HO-SAC) has also been introduced. A new Analysis of Similarity of extended HO-SAC and Differential Cryptanalysis has also been elaborated in this paper.A Simple Encryption Algorithmhttps://peerj.com/preprints/31282017-08-152017-08-15Joseph Keenan St. Pierre
In this paper I present a Simple Encryption Algorithm (SEAL), by which 128-bit long blocks can be quickly encrypted/decrypted. The algorithm is designed to run efficiently in software without any specialized hardware while still guaranteeing a strong degree of confidentiality. The cipher is composed entirely of simple bit-wise operations, such as the exclusive-or and circular shift, in addition to modular addition, thereby making it exceedingly easy to implement in most programming languages as well as efficient in terms of performance.
In this paper I present a Simple Encryption Algorithm (SEAL), by which 128-bit long blocks can be quickly encrypted/decrypted. The algorithm is designed to run efficiently in software without any specialized hardware while still guaranteeing a strong degree of confidentiality. The cipher is composed entirely of simple bit-wise operations, such as the exclusive-or and circular shift, in addition to modular addition, thereby making it exceedingly easy to implement in most programming languages as well as efficient in terms of performance.Secure trustless text processing of sensitive documentshttps://peerj.com/preprints/29942017-05-262017-05-26Flávio C CoelhoBruno Cuconato
Scaling up the analysis of sensitive or confidential documents frequently stumbles on the limited number of individuals with the necessary clearance to access the documents. The availability of cryptographic protocols compatible with text processing methods can greatly improve this situation allowing for the automated processing of large corpora of confidential documents by ``untrusted'' third-parties. In this paper we propose a protocol which allows for secure outsourcing of text analytics tasks without compromising the confidentiality of documents. The method scales to large corpora, and presents linear time complexity on the size of the corpus.
Scaling up the analysis of sensitive or confidential documents frequently stumbles on the limited number of individuals with the necessary clearance to access the documents. The availability of cryptographic protocols compatible with text processing methods can greatly improve this situation allowing for the automated processing of large corpora of confidential documents by ``untrusted'' third-parties. In this paper we propose a protocol which allows for secure outsourcing of text analytics tasks without compromising the confidentiality of documents. The method scales to large corpora, and presents linear time complexity on the size of the corpus.A comprehensive investigation of visual cryptography and its role in secure communicationshttps://peerj.com/preprints/26822017-01-202017-01-20Elham ShahabHadi Abdolrahimpour
Secret sharing approach and in particular Visual Cryptography (VC) try to address the security issues in dealing with images. In fact, VC is a powerful technique that combines the notions of perfect ciphers and secret sharing in cryptography. VC takes an image (secret) as an input and encrypts (divide) into two or more pieces (shares) that each of them can not reveal any information about the main input. The decryption way in this scenario is done through superimposing shares on top of each other to receive the input image. No computer participation is required, thus showing one of the distinguishing features of VC. It is claimed that VC is a unique technique in the sense that the encrypted message can be decrypted directly by the human visual system.
Secret sharing approach and in particular Visual Cryptography (VC) try to address the security issues in dealing with images. In fact, VC is a powerful technique that combines the notions of perfect ciphers and secret sharing in cryptography. VC takes an image (secret) as an input and encrypts (divide) into two or more pieces (shares) that each of them can not reveal any information about the main input. The decryption way in this scenario is done through superimposing shares on top of each other to receive the input image. No computer participation is required, thus showing one of the distinguishing features of VC. It is claimed that VC is a unique technique in the sense that the encrypted message can be decrypted directly by the human visual system.Technology to limit the available number of chosen-plaintexthttps://peerj.com/preprints/25342016-10-242016-10-24Ichiroh Kazawa
This technology sets an upper limit on the number of available pairs for chosen-plaintext and ciphertext in any chosen-plaintext-attack (CPA).By applying the typical implementation of 128-bit encryption, all CPAs cannot use more than 16 chosen-plaintexts.It does not encrypt the plaintext directly with this technique.256 kinds of variations are created from the plaintext.
It then chooses one variation at random to encrypt.
Unless the encryption key is used in decryption, it is impossible to find out which of the 256 kinds of variations was used for the ciphertext.
A CPA when used for multiple chosen-plaintexts would need to repeat the comparison for the total amount of combinations of the chosen-plaintext.If the CPA increases the total amount of chosen-plaintexts by one, the number of generated encryption keys increased by 256 times.256^{16} (== 2^{128}) encryption keys will be generated from the 16 chosen-plaintexts.Since the the total key possibilities generated exceed the total number of encryption keys, it is not possible for CPA to win with a brute force attack.RC4 is no longer recommended.However, the compactness of RC4 in embedded devices (e.g. RF-ID) has a big advantage in regards to block ciphers such as AES.
Secret Key Size(bit length) / Variations Count(bit length) > Chosen Plaintexts Count(useable count)
** Industrial significance **
RC4 is no longer recommended.
However, the compactness of RC4 in embedded devices (e.g. RF-ID) has a big advantage in regards to block ciphers such as AES.
RC4 can regain its security with this technology.
Compacting embedded devices will lead mainly to the reduction of costs.
It is believed that this technology will contribute greatly to the IoT.
”XORveR”, is this technologies codename.
This technology sets an upper limit on the number of available pairs for chosen-plaintext and ciphertext in any chosen-plaintext-attack (CPA).By applying the typical implementation of 128-bit encryption, all CPAs cannot use more than 16 chosen-plaintexts.It does not encrypt the plaintext directly with this technique.256 kinds of variations are created from the plaintext.It then chooses one variation at random to encrypt.Unless the encryption key is used in decryption, it is impossible to find out which of the 256 kinds of variations was used for the ciphertext.A CPA when used for multiple chosen-plaintexts would need to repeat the comparison for the total amount of combinations of the chosen-plaintext.If the CPA increases the total amount of chosen-plaintexts by one, the number of generated encryption keys increased by 256 times.256^{16} (== 2^{128}) encryption keys will be generated from the 16 chosen-plaintexts.Since the the total key possibilities generated exceed the total number of encryption keys, it is not possible for CPA to win with a brute force attack.RC4 is no longer recommended.However, the compactness of RC4 in embedded devices (e.g. RF-ID) has a big advantage in regards to block ciphers such as AES.Secret Key Size(bit length) / Variations Count(bit length) > Chosen Plaintexts Count(useable count)** Industrial significance **RC4 is no longer recommended.However, the compactness of RC4 in embedded devices (e.g. RF-ID) has a big advantage in regards to block ciphers such as AES.RC4 can regain its security with this technology.Compacting embedded devices will lead mainly to the reduction of costs.It is believed that this technology will contribute greatly to the IoT.”XORveR”, is this technologies codename.