Acknowledgements

From the above algorithm, first convert the integer to binary representation, and then from the right partition every 26,25,26,25,...,k, with 0 ≤ k ≤ 25, as an example of an integer with length of binary representation is 231, then partition from the right 26,25,26,25,26,25,26,25,26,1. Every partition states the value sum of d(i)2<sup>i</sup><sup>1</sup>

with d(i) is the value of the order of the binary representation that is either 0 or 1.

coefficient x1 would be the value 4851911. Thus, the number 325606250916557 represented by radix 225.5 would be 4851911x + 15477453. Also, we can use.

After we have converted any integer, there is an additional problem when the coefficient of radix 225.5 exceeds our definition. For this problem, Bernstein [1] has

Communication systems in the future are expected to interact between diverse types of devices. This allows the user to construct a personal distributed environment using a combination of different communication technologies. The security of

Nowadays instant messaging is popular for personal and business communications instead of short messages (SMS) on mobile devices. However, most mobile messaging applications do not protect confidentiality or message integrity. Supervision over private communications conducted by the NSA motivates many people to use alternative messaging solutions for security and privacy of communication on the Internet. A messaging app that claims to be secure instant messaging and has

Elliptic curve cryptosystem (ECC) is a public-key cryptography suitable for use in environments with limited resources such as mobile devices and smart cards. In cryptography, Curve25519 is an elliptic curve that offers 128 security bits and is designed for use in the Elliptic Curve Diffie-Hellman (ECDH) key agreement key design scheme. This curve is one of the fastest ECC curves and more resistant to the

<sup>2</sup> = x<sup>3</sup> + 48666x<sup>2</sup> + x, a Montgomery curve,

In the TextSecure application, Curve25519 is used for key exchanges and authentication. However, in this paper we show that Curve25519 can also be implemented in simplified Elliptic Curve Integrated Encryption Scheme (S-ECIES). Therefore Curve25519 serves for key exchange, authentication, encryption, and decryption. As Curve25519 is built in such a way as to avoid potential attacks on implementation and avoid side channel attacks and random number generator

over the prime field 2255–19. This protocol uses elliptic point compression (only the X-abscissa), allowing for efficient use of Montgomery ladder for ECDH, which uses

issues, one may expect more secure communication systems.

The curve being used in this paper is y

transmitted data between these devices is a very important aspect.

. Example: Suppose we have a 15-digit number, 325606250916557, which has binary representation "1001010000010001100 01110 01110 11000 01010 10110 01101." For integers, 325606250916557 has two partitions, i.e., 00111011000010101011001101 and 10010100000100011000111. Therefore, the coefficient of x0 is 0.225 + 0.224 + 1.223 +

, which if we calculated would be the value 15477453. In the same way,

Also, the j-th partition is the coefficient of x<sup>j</sup><sup>1</sup>

Theorizing STEM Education in the 21st Century

addition and multiplication in radix 225.5.

attracted a lot of attention is TextSecure.

weak number random generator.

6. Conclusion

only XZ coordinates.

196

... + 0.21 + 1.20

5. Applications

already provided a solution.

,

This research is funded by Hibah Riset KK ITB 2017.
