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2018, 5(3)
HighLights More»   
· Cloud-based RFID Mutual Authentication Protocol——CHEN M M, DONG Q K, LI L L}
· Implementation Scheme of SIS Lattice Signature Against Side Channel Attack——LI Z C, SUN Y F, YANG Y T, ZHANG J M, YANG W, LIANG L
· Simulator of Quantum Computer Using Classical Computer——
· Homomorphically Encrypted Arithmetic Operations over Symmetric Ternary Coding——FU H J, CAI B, XIANG H, SANG J
·

Similar Search Balanced Binary Tree Based Multi-keyword Ranked Searchable Scheme——CHEN L X, CHEN Z C

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  Journal of Cryptologic Research--2018, 5 (3)   Published: 22 June 2018
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Articles
Cloud-based RFID Mutual Authentication Protocol Hot!
CHEN M M, DONG Q K, LI L L}
Journal of Cryptologic Research. 2018, 5 (3): 231-241. ;  doi: 10.13868/j.cnki.jcr.000234
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Show Abstract ( 141 )

With the development of the Internet of things and cloud computing, a large number of objects access to the internet through RFID technology. Cloud-based RFID system adopts the way of renting cloud database on demand, which can reduce the costs of system maintenance, the system is very suitable for the small and medium-sized enterprises, therefore, it gets wide attention. However, the security and privacy problems of cloud-based RFID systems are more serious, the link between the reader and the cloud database is no longer secure, the tag identity and data privacy of RFID cannot be exposed to cloud service providers. This paper proposes a cloud-based RFID mutual authentication protocol, the protocol is designed based on the hash function, it realizes the authentication between the reader and tag, at the same time, it ensures the security of the data transmission between the reader and cloud database, moreover, it can protect the anonymity of the reader, and reduce the computational complexity of the tag. Security analysis shows that the protocol satisfies security requirements, such as untraceability, forward security, withstand replay attack, de-synchronization attack and denial of service attack, etc. The formally analysis with BAN logic further indicates the protocol satisfies the mutual authentication, and can withstand replay attack, at the same time, the paper analyses and proves other security requirements. Compared with other several cloud-based schemes, the proposed protocol has advantages in tag's computation cost and communication cost of the whole protocol.

Implementation Scheme of SIS Lattice Signature Against Side Channel Attack Hot!
LI Z C, SUN Y F, YANG Y T, ZHANG J M, YANG W, LIANG L
Journal of Cryptologic Research. 2018, 5 (3): 242-248. ;  doi: 10.13868/j.cnki.jcr.000235
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Show Abstract ( 99 )

 With the development of the quantum computer, the traditional digital signature schemes are challenged by the quantum attack, analysis and design of digital signature algorithms that can resist quantum computers are current research hotspots. In the actual execution of the cryptographic algorithms, it often faces the risk of side channel attacks. So, many factors need to be taken into consideration in designing a secure and effective cryptography algorithm. Lattice cryptography is a typical representative of post quantum algorithm, the digital signature algorithm based on lattice can posses security in the quantum environment, but it also face the thread of timing attack and first-order power attack and other side channel attacks in the real execution environment. In order to ensure the lattice cryptography having the ability to resist the side channel attacks, we propose an implementation scheme of SIS lattice signature against side channel attack. Through setting the parameters of Gauss sampling, and random segmentation of sampling samples, enlarging the range of sampling, it can have effective resistance against the Cache attack. We split the secret key in the signing process, this can obtain masking operation of the secret, and it can be effective in resisting the first-order differential power attack. The difficult problem which the SIS implementation scheme proposed in this paper is based on its provable security under the Random Oracle model, and this scheme can resist the Cache attack and first-order differential power attack, it can ensure the security of the key.

Simulator of Quantum Computer Using Classical Computer Hot!
Journal of Cryptologic Research. 2018, 5 (3): 249-261. ;  doi: 10.13868/j.cnki.jcr.000236
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Show Abstract ( 117 )

Quantum state superposition and entanglement enable a quantum computer's exponential speed-up in solving many crypto-significant hard problems, such as integer factorization, discrete logarithm, etc. In this paper, methods of modeling the quantum state superposition and entanglement, quantum bits and gates representations and multiple-bit computation prototype are given. Based on object-oriented Python, we provide a quantum simulator integrated with an API suite implementing the methods aforementioned. To ease the coding process, we designed a user-friendly interface, including realization of quantum circuits design, measurement result demonstration, statistic and other accessories. At the end of the paper, some experiments on quantum computing have been done with the software developed in this paper, and the experimental results are given. The experimental results are further analyzed with the principle of quantum computing to enhance the reader's understanding of quantum computing.

Homomorphically Encrypted Arithmetic Operations over Symmetric Ternary Coding Hot!
FU H J, CAI B, XIANG H, SANG J
Journal of Cryptologic Research. 2018, 5 (3): 262-270. ;  doi: 10.13868/j.cnki.jcr.000237
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Show Abstract ( 74 )

Fully homomorphic encryption can support the operation of any function of the ciphertext obtaining the result of the corresponding operation on the plaintext after decryption. Fully homomorphic encryption application needs to encode the data into plaintext strings by encoding, and then homomorphic encrypts the plaintext into a ciphertext and performs the function operation on the ciphertext. Then, decrypts the ciphertext, and finally decode the decryption results into the data type in the application. Different coding schemes have a great influence on the efficiency of fully homomorphic encryption applications. In this paper, the symmetric ternary coding method is applied to the fully homomorphic encryption application, and an integer symmetric ternary coding algorithm is designed. Meanwhile, the bitwise multiplication depth of integer addition, integer subtraction and integer multiplication under symmetric ternary coding is analyzed. Designed integer symmetric ternary coding arithmetic operations do not require the setting of the sign bits for the code, and the operation process is optimized according to the principle of reducing the number of bitwise multiplication depth. Finally, we use the HElib library to achieve the integer symmetric ternary encoding under the 10-bit homomorphism addition, homomorphic subtraction and homomorphism multiplication arithmetic, and the calculation period does not need Bootstrapping process. The experimental results show that the homomorphic arithmetic efficiency of integers under symmetric ternary coding is superior to binary coding.

Similar Search Balanced Binary Tree Based Multi-keyword Ranked Searchable Scheme Hot!

CHEN L X, CHEN Z C
Journal of Cryptologic Research. 2018, 5 (3): 271-285. ;  doi: 10.13868/j.cnki.jcr.000238
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Show Abstract ( 64 )

Cloud storage enables users to outsource their sensitive data to the cloud server to facilitate data management. However, when the data is stored in the third party server, it is no longer fully controllable. So the protection of data privacy is extremely important. Usually, users encrypt their data first and then store it on the cloud server to ensure data privacy. However, after data is encrypted, the traditional plaintext keyword search is unavailable. In this paper, we propose a similar search balanced binary tree based multi-keyword ranked searchable encryption scheme (SMRSS). The core idea is to construct similar file sets and stores the similar Top-k files with high relevant score in the leaf node of the index tree. When users query for Top-k files, it can get the highest similar files at the fastest speed. Meanwhile, it utilizes vector space model and TF-IDF weighted statistical method to construct an index, and uses Euclidean distance to determine similar files. As the index structure is based on the balanced binary tree, the search complexity is sub-linear. The experimental results show that, compared with the EDMRS scheme, the SMRSS scheme greatly improves the search efficiency while ensuring equivalent accuracy and security.

Security Deduplication Method of Encrypted Data Without Any Additional Server Hot!
ZHANG S G, XIAN H Q, WANG L M, LIU H Y, HOU R T
Journal of Cryptologic Research. 2018, 5 (3): 286-296. ;  doi: 10.13868/j.cnki.jcr.000239
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Show Abstract ( 79 )

Deduplication has been widely used in public cloud services. This technology means that only one copy of the same data is stored in the cloud. If there is a duplicate copy, the cloud deduplicates it and creates a link for the uploader to access the initial data copy. The same data hold the same Hash value which makes deduplication of plaintext data much simpler. However, in order to protect data privacy, most users choose to use a private key to encrypt data and then outsource to the cloud. Due to the diversity of user keys, a same plaintext may be encrypted into different ciphertexts, and the cloud cannot perform deduplication in this case. Most existing solutions rely on third-party servers, resulting in their low security and execution efficiency. This study proposes a deduplication scheme that does not require trusted third parties. A password authentication key exchange protocol and the bilinear mapping are used to build an encryption data redundancy identification algorithm to securely verify whether different encrypted data originate from the same plaintext data. The homomorphic encryption algorithm is adopted to design the secure encryption key deliver algorithm, in which the initial uploader can safely deliver the encryption key to the subsequent uploader via the cloud. Users with the same data are able to obtain the same encryption key, and the cloud server can achieve the deduplication of encrypted data. Security analysis and performance evaluation shows the scheme's high security and implementation efficiency.

Preface on Special Topics
Preface of Elliptic Curve Cryptography Column (in Chinese and in English)#br# Hot!
XU M Z
Journal of Cryptologic Research. 2018, 5 (3): 297-300. ;  doi: 10.13868/j.cnki.jcr.000240
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Show Abstract ( 113 )

Elliptic curve is an important mathematical object with beautiful properties and rich connotations. Its theoretical research is very abstruse, connecting to number theory, algebra, geometry, and complex function theory. While in recent decades, its applications in cryptography are becoming increasingly important.

 

Since Diffie and Hellman put forward the idea of public key cryptography in 1976,

many public key systems have been proposed, the security of which is all based on a hard mathematical problem. In 1985, Koblitz and Miller independently introduced elliptic curves over finite field to design public key cryptography. Since then, three kinds of mathematical problems become the basis of  public key cryptography:

(1) Big number factorization problems, such as RSA;

(2) Discrete logarithmic problems over finite fields, such as EIGamal encryption  and digital signature scheme, Diffie-Hellman key exchange and Schnorr signature scheme;

(3) Elliptic curve discrete logarithmic problems over finite fields, such as elliptic curve Diffie-Hellman key exchange,  elliptic curve digital signature scheme, and elliptic curve Schnorr signature scheme.

 

With the great popularity of public key cryptography, these mathematical problems have attracted a lot of attention and many important algorithms have been developed.

Now there exists sub-exponential time algorithm (eg. GNFS) for the first two types of questions, which makes RSA, DH, and similar schemes more and more vulnerable. In order to guarantee security, the larger size of modulus or finite fields are needed.

Currently, 1024 or 2048 bit sizes are commonly used. However, there has been little progress in solving general elliptic curve discrete logarithmic problems.

As a result, elliptic curve cryptography has the highest level of security per bit. For example, the 160-bit(210-bit) for elliptic curve cryptography has the same security strength as the 1024-bit(2048-bit) for RSA, thus the advantage of elliptic curve cryptography is fully demonstrated.

 

With the wide applications of elliptic curve cryptography, elliptic curve cryptography has become the focus in academia, which fully enriches the research on algorithm number theory, PKC, and even fundamental mathematics.

 

In the wake of the well known one-round three-way key exchange protocol proposed by Joux in 2000, numerous novel and important cryptographic schemes are built based on bilinear pairings on elliptic curves. The greatest breakthrough is the ID-based  encryption proposed by Sakai, Ohgishi, Kasahara, Boneh, and Franklin, solving Shamir's open problem in 1984. The other important breakthroughs include ID-based signatures, short signatures, zero-knowledge proofs, and so on. It should be noted that practical bilinear pairings are all based on Weil pairings, Tate pairings or their variants defined on elliptic curves over finite fields, so such pairing-based cryptography can also be regarded as the applications of elliptic curves in cryptography.

 

In this elliptic curve cryptography column, 3 papers are chosen involving 3 research directions in  elliptic curve cryptography. All of them have great application value.

 

The first paper is about deterministic encoding problems from finite fields into elliptic curves. Such problems are very common in practical. For example, many elliptic curve cryptographic schemes need Hash functions from finite fields into elliptic curves, then how to ensure the security is inherited? Then the Hash functions from bit-strings into elliptic curves should be constructed, which are indifferentiable from random oracles. In addition, by constructing injective maps, censorship circumvention can be achieved.

 

There has existed many research results on this problem and He Xiao-Yang et al. have done a lot of them. Their paper ``On Construction and Application of Deterministic Encoding Functions into Elliptic Curves" is a solid overview for this problem, and it points out that  encoding into hyperelliptic curves can be further studied.

 

 

The second paper is on the transform of  equations of elliptic curve. Elliptic curves have kinds of algebraic equations, such as Weierstrass form, Edwards form, etc. Compared with the classical Weierstrass form, Edwards form has more advantages from a point of view of computational efficiency and safety. It is very easy to convert the Edwards form into the Weierstrass form for elliptic curves over binary fields, but the opposite is not straightforward. Zhang Jing-Wei and Zhao Chang-An's paper ``Algorithm of Converting Weierstrass Form into Edwards Form for Elliptic Curves over Binary Fields" constructs a birational transformation algorithm between Weierstrass form and Edwards form, which has a deterministic polynomial time complexity. Without requiring any additional condition, and the only a small amount of computation is involved in the proposed algorithm. Using this result, we can convert equations between Weierstrass form and Edwards form,  so as to make full use of the advantages of Edwards form and achieve the higher efficiency and security.

 

The last paper is about the construction of pairing-based cryptography. To improve the efficiency of practical applications of pairings, it is required to solve two closely related problems: constructing pairing-friendly curves, and improving the efficiency and flexibility of algorithms to compute pairings. Zhang Meng et al. have systematically studied the construction of pairing-friendly elliptic curves and found a new practical family. ``Constructing Optimal Pairings for Menezes-128 Security Level" is a further study of construction based on the new family. With the tremendous progress made on discrete logarithm problem over finite  fields, AES-128 security level should be replaced by Menezes-128 security level. For example, the popular BN curves satisfy AES-128 security level, but fail to satisfy Menezes-128 security level. Using lattice algorithm, twist, Frobenius map, and other means, they construct optimal pairings for Menezes-128 security level on the basis of the new family. It would serve as a new choice for the practical pairing-based applications.

 

At last, I hope that this column will play a role in attracting more and more people to be interested in elliptic curve cryptography, and further devote themselves to the studies of elliptic curve cryptography.

Reviews in Special Topics
On Construction and Application of Deterministic Encoding Functions into Elliptic Curves Hot!
HE X Y, YU W, WANG K P
Journal of Cryptologic Research. 2018, 5 (3): 301-314. ;  doi: 10.13868/j.cnki.jcr.000241
Full Text: HTML (1 KB)  PDF (610 KB)  ( 86 )
Show Abstract ( 95 )

In this paper, we summarize deterministic encodings from finite field $\fq$ into elliptic curves. Based on these encodings, various Hash functions from bit-strings into elliptic curves are constructed, which are indifferentiable from random oracles. Such Hash functions can be applied in plenty of cryptographic protocols. For instance, some identity-based cryptosystems can utilize these Hash functions to generate public-keys efficiently. On the other side, by constructing injective maps from large subset of a finite field to elliptic curves, one can present points on curves as strings with distribution indistinguishable from the uniform distribution of bit strings, hence censorship circumvention can be achieved when transmitting public keys. When $q\equiv 3\pmod 4$,   SWU algorithm and its varients are applied to construct deterministic encodings into elliptic curves, while Icart's algorithm and its varients are applied in the case of  $q\equiv 2\pmod 3.$ The time complexity of these algorithms are all $\mathcal{O}(\log^3q).$ For some hyperelliptic curves, deterministic encodings can also be constructed.

Articles in Special Topics
Algorithm of Converting Weierstrass Form into Edwards Form for Elliptic Curves over Binary Fields Hot!
ZHANG J W, ZHAO C A
Journal of Cryptologic Research. 2018, 5 (3): 315-323. ;  doi: 10.13868/j.cnki.jcr.000242
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Show Abstract ( 71 )

Elliptic curves over finite fields have found many applications in public key cryptography, such as elliptic curve cryptosystems (ECC), identity-based encryption, isogeny-based Diffie-Hellman key exchange, etc. Elliptic curves have a variety of algebraic equations including Weierstrass form, Edwards form, Huff form, Hessian form, etc. Different forms of elliptic curves have their own merits.  Compared with the classical Weierstrass form, the Edwards form has more advantages with respect to efficiency and security. However, the parameters of traditional ECC used in standards are given in the Weierstrass form. It is inconvenient for engineers to implement cryptographic algorithms in the Edwards form.  This paper gives an algorithm of converting the Weierstrass form into the Edwards form for elliptic curves over binary fields. The converting process makes use of the Shallue-Woestijne algorithm and the halving a rational point algorithm. The proposed algorithm has a deterministic polynomial time complexity and does not require any additional condition compared with the previous results. In addition, only a small amount of computation is required in the proposed algorithm. An example is illustrated explicitly for the conversion process from the Weierstrass form into the Edwards form in the Appendix.

Constructing Optimal Pairings for Menezes-128 Security Level Hot!
ZHANG M, WANG S, GUO Z Z
Journal of Cryptologic Research. 2018, 5 (3): 324-334. ;  doi: 10.13868/j.cnki.jcr.000243
Full Text: HTML (1 KB)  PDF (564 KB)  ( 54 )
Show Abstract ( 61 )

Bilinear pairings are important tools in cryptography. Based on bilinear pairings, numerous novel and important cryptographic schemes are built, such as ID-based encryption, ID-based signature, one-round three-way key exchange protocols. The security of these schemes are all based on the hardness of discrete logarithms over elliptic curves and finite fields. However, in recent years, significant progress has been made on discrete logarithm problem over finite fields. As a result, some security standards no longer fit, for example, AES-128's security level should be replaced by Menezes-128's security level. In this paper, we firstly analyze the necessity of changing AES-128's security to Menezes-128's level. Then according to the steps of pairing construction and computation in practice, we consider the concrete implementation of optimal pairings suitable for Menezes-128's security level. Using lattice algorithm, twist, Frobenius map and other means, we construct optimal pairings for Menezes-128's security level at present on the basis of a new family of pairing-friendly elliptic curves with $k=12$、$ \rho=1.5$. It serves as a new choice for the practical pairing-based applications.

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