In this paper we propose a double block length hash function called MR-MMO. Our scheme satisfies two calls of (n, 2n) blockcipher and can compress 3n bits to 2n bits (n = 128 bits). The Collision Resistance (CR) and Preimage Resistance (PR) of MR-MMO are respectively 2 126.70 and 2 252.5 . Surprisingly, the collision security bound of our scheme is the best in compare with other existing schemes. We use a single key scheduling for each compression function which is great in respect of cost and time. Additionally, it can be said that the proof technique of Weimar-DM, Tandem-DM, Hirose-DM are based on Ideal Cipher Model (ICM) while we use Weak Cipher Model (WCM) tool. Davies Meyer (DM) mode is used in the above all schemes, we also made a change using Matyas Meyer Oseas (MMO) mode. It is also obvious that the proof technique of our scheme is very simple, straightforward and easy to understand.

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SUMMARYA cryptographic hash is an important tool in the area of a modern cryptography. It comprises a compression function, where the compression function can be built by a scratch or blockcipher. There are some familiar schemes of blockcipher compression function such as Weimar, Hirose, Tandem, Abreast, Nandi, ISA-09. Interestingly, the security proof of all the mentioned schemes are based on the ideal cipher model (ICM), which depends on ideal environment. Therefore, it is desired to use such a proof technique model, which is close to the real world such as weak cipher model (WCM). Hence, we proposed an (n, 2n) blockcipher compression function, which is secure under the ideal cipher model, weak cipher model and extended weak cipher model (ext.WCM). Additionally, the majority of the existing schemes need multiple key schedules, where the proposed scheme and the Hirose-DM follow single key scheduling property. The efficiency-rate of our scheme is r = 1/2. Moreover, the number of blockcipher call of this scheme is 2 and it runs in parallel. key words: cryptographic hash, blockcipher, ideal cipher model, weak cipher model, collision and preimage resistance

An authentication encryption (AE) scheme satisfies to transfer an authenticated data between 2 parties or more. There are vast applications of the AE such as access control, encryption, enhancing trust between multiple parties, and assure the originality of a message. However, the main challenge of the AE is to maintain low-cost features for its construction. Furthermore, there is another emerging issue of Internet of Things (IoT) in the field of data and network communication.The numbers of application of the IoT are increasing expeditiously, where various kinds of device have been used such as IoT-end device, constrained device, and RfID. Moreover, the main challenge of the IoT-end devices and resource constrained devices is to keep a certain level of security bound including minimum cost. However, the IoT-end devices, resource constrained devices, and RfID have lack of resources such as memory, power, and processors. Interestingly, the AE can play a vital role between data acquisition (sensors, actuators) and data aggregation of usual platform of the IoT. Thus, the construction of the AE should satisfy the properties of low-cost, least resources, and less operating-time. Though, there are many familiar constructions of AE such as OTR, McOE, POE, OAE, APE, COPE, CLOC, and SILK but most of the schemes depend on the features of nonce and associate data. In the aspect of security, the usage of nonce and associated data are adequate.However, these 2 features increase the overhead cost. Therefore, we propose a simple construction of IV-based AE where blockcipher compression function is used as encryption function. Our proposed scheme's efficiency-rate is 1 with reasonable privacy-security bound. In addition, it can encrypt arbitrary length of message in each iteration without padding.

Summary A constrained device is an emerging technology that has enormous applications in our daily life such as access control, inventory control, luggage tracking, bar‐code reader, and IoT. However, it has certain drawbacks of low memory and less computing power. Thus, one of the cracking challenges is to provide efficient and secure cryptographic solution for the constrained device in the aspect of security issue. An (n,n) blockcipher‐based cryptographic compression function is applicable to provide provable security to the constrained device. Though, there are many constructions of (n,n) blockcipher such as MDC‐2, MDC‐4, MJH, Bart‐12, and SKS‐15. However, most of the familiar schemes are not suitable for short and variable message encryption without padding because of their internal structures. Furthermore, the security margin is provided based on blocklength rather than the flexible size of message. In this paper, we present two different (n,n) blockcipher compression function schemes. The first scheme (FS) satisfies better efficiency such as less call of blockcipher, less key scheduling, and higher efficiency rate. On the contrary, the second scheme (SS) has upper security bound. Moreover, both of the schemes are suitable for small and variable message encryption (message size =   tn|t < 1,n:blocklength), which is handy for the constrained device. The collision and preimage security bound of the FS are O(2tn/2) and O(2tn). In addition, the SS's collision resistance and preimage resistance are bounded by O(2tn) and O(22tn). Moreover, the efficiency rate of the proposed two schemes are respectively t and t/3. The numbers of key scheduling are 2 for the constructions of FS and SS. We use two calls of blockcipher in the FS. On the contrary, three calls of blockcipher are used in the SS. Copyright © 2016 John Wiley & Sons, Ltd.