scholarly journals A New Class of Strongly Asymmetric PKA Algorithms: SAA-5

Cryptography ◽  
2019 ◽  
Vol 3 (1) ◽  
pp. 9
Author(s):  
Luigi Accardi ◽  
Satoshi Iriyama ◽  
Koki Jimbo ◽  
Massimo Regoli
Keyword(s):  
Computational Complexity ◽  
Key Agreement ◽  
Public Key ◽  
Discrete Logarithms ◽  
New Class ◽  
Diffie Hellman ◽  
Class B ◽  
Shared Key

A new class of public key agreement (PKA) algorithms called strongly-asymmetric algorithms (SAA) was introduced in a previous paper by some of the present authors. This class can be shown to include some of the best-known PKA algorithms, for example the Diffie–Hellman and several of its variants. In this paper, we construct a new version of the previous construction, called SAA-5, improving it in several points, as explained in the Introduction. In particular, the construction complexity is reduced, and at the same time, robustness is increased. Intuitively, the main difference between SAA-5 and the usual PKA consists of the fact that in the former class, B (Bob) has more than one public key and A (Alice) uses some of them to produce her public key and others to produce the secret shared key (SSK). This introduces an asymmetry between the sender of the message (B) and the receiver (A) and motivates the name for this class of algorithms. After describing the main steps of SAA-5, we discuss its breaking complexity assuming zero complexity of discrete logarithms and the computational complexity for both A and B to create SSK.

scholarly journals Implementation of a New Strongly-Asymmetric Algorithm and Its Optimization

Cryptography ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 21
Author(s):  
Koki Jimbo ◽  
Satoshi Iriyama ◽  
Massimo Regoli
Keyword(s):  
General Framework ◽  
Key Agreement ◽  
Public Key ◽  
Security Level ◽  
The Public ◽  
High Speeds ◽  
Diffie Hellman ◽  
New Public ◽  
Public Keys ◽  
Free Parameters

A new public key agreement (PKA) algorithm, called the strongly-asymmetric algorithm (SAA-5), was introduced by Accardi et al. The main differences from the usual PKA algorithms are that Bob has some independent public keys and Alice produces her public key by using some part of the public keys from Bob. Then, the preparation and calculation processes are essentially asymmetric. This algorithms has several free parameters more than the usual symmetric PKA algorithms and the velocity of calculation is largely dependent on the parameters chosen; however, the performance of it has not yet been tested. The purpose of our study was to discuss efficient parameters to share the key with high speeds in SAA-5 and to optimize SAA-5 in terms of calculation speed. To find efficient parameters of SAA-5, we compared the calculation speed with Diffie–Hellman (D-H) while varying values of some parameters under the circumstance where the length of the secret shared key (SSK) was fixed. For optimization, we discuss a more general framework of SAA-5 to find more efficient operations. By fixing the parameters of the framework properly, a new PKA algorithm with the same security level as SAA-5 was produced. The result shows that the calculation speed of the proposed PKA algorithm is faster than D-H, especially for large key lengths. The calculation speed of the proposed PKA algorithm increases linearly as the SSK length increases, whereas D-H increases exponentially.

Key Management

2011 ◽  
pp. 88-113
Author(s):  
Chuan-Kun Wu
Keyword(s):  
Secret Sharing ◽  
Key Management ◽  
Key Agreement ◽  
Public Key ◽  
Key Escrow ◽  
The Public ◽  
Cryptographic Algorithm ◽  
Diffie Hellman ◽  
Public Networks ◽  
Active Attacks

In secure communications, key management is not as simple as metal key management which is supposed to be in a key ring or simply put in a pocket. Suppose Alice wants to transmit some confidential information to Bob over the public networks such as the Internet, Alice could simply encrypt the message using a known cipher such as AES, and then transmit the ciphertext to Bob. However, in order to enable Bob to decrypt the ciphertext to get the original message, in traditional cipher system, Bob needs to have the encryption key. How to let Alice securely and efficiently transmit the encryption key to Bob is a problem of key management. An intuitive approach would be to use a secure channel for the key transmission; this worked in earlier years, but is not a desirable solution in today’s electronic world. Since the invention of public key cryptography, the key management problem with respect to secret key transmission has been solved, which can either employ the Diffie-Hellman key agreement scheme or to use a public key cryptographic algorithm to encrypt the encryption key (which is often known as a session key). This approach is secure against passive attacks, but is vulnerable against active attacks (more precisely the man-in-the-middle attacks). So there must be a way to authenticate the identity of the communication entities. This leads to public key management where the public key infrastructure (PKI) is a typical set of practical protocols, and there is also a set of international standards about PKI. With respect to private key management, it is to prevent keys to be lost or stolen. To prevent a key from being lost, one way is to use the secret sharing, and another is to use the key escrow technique. Both aspects have many research outcomes and practical solutions. With respect to keys being stolen, another practical solution is to use a password to encrypt the key. Hence, there are many password-based security protocols in different applications. This chapter presents a comprehensive description about how each aspect of the key management works. Topics on key management covered by this chapter include key agreement, group-based key agreement and key distribution, the PKI mechanisms, secret sharing, key escrow, password associated key management, and key management in PGP and UMTS systems.

On a class of strongly asymmetric PKA algorithms

2015 ◽  
Vol 9 (3) ◽  
Author(s):  
Luigi Accardi ◽  
Massimo Regoli
Keyword(s):  
Matrix Model ◽  
Key Agreement ◽  
Key Exchange ◽  
Public Key ◽  
Discrete Logarithms ◽  
Essential Ingredient ◽  
Cryptographic Algorithms ◽  
Exchange Algorithms ◽  
The Matrix

AbstractIn the papers [New features for public key exchange algorithms, in: 18-th International ICWG Meeting (Krakow 2011)], [Strongly asymmetric PKD cryptographic algorithms: An implementation using the matrix model, in: Proceedings ISEC Conference (Shizuoka 2011)] a new scheme to produce public key agreement (PKA) algorithms was proposed and some examples based on polynomials (toy models) were discussed. In the present paper we introduce a non-commutative realization of the above mentioned scheme and prove that non-commutativity can be an essential ingredient of security in the sense that, in the class of algorithms constructed, under some commutativity assumptions on the matrices involved, we can find a breaking strategy, but dropping these assumptions we can not, even if we assume, as we do in all the attacks discussed in the present paper, that discrete logarithms have zero cost.

Key Management

2013 ◽  
pp. 728-753
Author(s):  
Chuan-Kun Wu
Keyword(s):  
Secret Sharing ◽  
Key Management ◽  
Key Agreement ◽  
Public Key ◽  
Key Escrow ◽  
The Public ◽  
Cryptographic Algorithm ◽  
Diffie Hellman ◽  
Public Networks ◽  
Active Attacks

In secure communications, key management is not as simple as metal key management which is supposed to be in a key ring or simply put in a pocket. Suppose Alice wants to transmit some confidential information to Bob over the public networks such as the Internet, Alice could simply encrypt the message using a known cipher such as AES, and then transmit the ciphertext to Bob. However, in order to enable Bob to decrypt the ciphertext to get the original message, in traditional cipher system, Bob needs to have the encryption key. How to let Alice securely and efficiently transmit the encryption key to Bob is a problem of key management. An intuitive approach would be to use a secure channel for the key transmission; this worked in earlier years, but is not a desirable solution in today’s electronic world. Since the invention of public key cryptography, the key management problem with respect to secret key transmission has been solved, which can either employ the Diffie-Hellman key agreement scheme or to use a public key cryptographic algorithm to encrypt the encryption key (which is often known as a session key). This approach is secure against passive attacks, but is vulnerable against active attacks (more precisely the man-in-the-middle attacks). So there must be a way to authenticate the identity of the communication entities. This leads to public key management where the public key infrastructure (PKI) is a typical set of practical protocols, and there is also a set of international standards about PKI. With respect to private key management, it is to prevent keys to be lost or stolen. To prevent a key from being lost, one way is to use the secret sharing, and another is to use the key escrow technique. Both aspects have many research outcomes and practical solutions. With respect to keys being stolen, another practical solution is to use a password to encrypt the key. Hence, there are many password-based security protocols in different applications. This chapter presents a comprehensive description about how each aspect of the key management works. Topics on key management covered by this chapter include key agreement, group-based key agreement and key distribution, the PKI mechanisms, secret sharing, key escrow, password associated key management, and key management in PGP and UMTS systems.

scholarly journals Cryptanalysis of Kowada-Machado key exchange protocol

2018 ◽  
Vol 4 (1) ◽  
pp. 12
Author(s):  
M Coutinho ◽  
T C de Souza Neto ◽  
Robson De Oliveira Albuquerque ◽  
Rafael Timóteo de Sousa Júnior
Keyword(s):  
Recent Work ◽  
Open Problem ◽  
Key Exchange ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Shared Key ◽  
Diffie Hellman Key Exchange

A non-interactive key exchange (NIKE) protocol allows N parties who know each other’s public key to agree on a symmetric shared key without requiring any interaction. A classic example of such protocol for N = 2 is the Diffie-Hellman key exchange. Recently, some techniques were proposed to obtain a NIKE protocol for N parties, however, it is still considered an open problem since the security of these protocols must be confirmed. In a recent work, Kowada and Machado [1] proposed a protocol that solves the NIKE problem for N parties. However, this work found security problems in the proposed solution and implemented an efficient attack to their protocol demonstrating that their key-exchange scheme is insecure.

scholarly journals New Subclass Framework and Concrete Examples of Strongly Asymmetric Public Key Agreement

2021 ◽  
Vol 11 (12) ◽  
pp. 5540
Author(s):  
Satoshi Iriyama ◽  
Koki Jimbo ◽  
Massimo Regoli
Keyword(s):  
Computational Efficiency ◽  
Key Agreement ◽  
Necessary Conditions ◽  
Key Exchange ◽  
Public Key ◽  
High Security ◽  
Public Keys ◽  
Inclusion Relations ◽  
Shared Key

Strongly asymmetric public key agreement (SAPKA) is a class of key exchange between Alice and Bob that was introduced in 2011. The greatest difference from the standard PKA algorithms is that Bob constructs multiple public keys and Alice uses one of these to calculate her public key and her secret shared key. Therefore, the number of public keys and calculation rules for each key differ for each user. Although algorithms with high security and computational efficiency exist in this class, the relation between the parameters of SAPKA and its security and computational efficiency has not yet been fully clarified. Therefore, our main objective in this study was to classify the SAPKA algorithms according to their properties. By attempting algorithm attacks, we found that certain parameters are more strongly related to the security. On this basis, we constructed concrete algorithms and a new subclass of SAPKA, in which the responsibility of maintaining security is significantly more associated with the secret parameters of Bob than those of Alice. Moreover, we demonstrate 1. insufficient but necessary conditions for this subclass, 2. inclusion relations between the subclasses of SAPKA, and 3. concrete examples of this sub-class with reports of implementational experiments.

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