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"ABSTRAKTujuan utama dari keamanan komunikasi adalah mencegah data pesan dari akses pihak ketiga. Solusi dari masalah tersebut adalah menerapkan enkripsi End-to-end. Algoritma enkripsi Elliptic Curve Cryptography (ECC) cocok digunakan sebagai metode enkripsi End-to-end pada sistem komunikasi digital termasuk aplikasi chat. ECC adalah jenis kriptografi kunci publik yang mendasarkan keamanannya pada permasalahan matematis dari kurva eliptik, ECC mempunyai tingkat keamanan yang setara dengan RSA menggunakan kunci berukuran lebih kecil. Penelitian ini membahas perancangan dan implementasi dari algoritma enkripsi dan dekripsi yang menerapkan kriptografi ECC sebagai metode enkripsi End-to-end pada aplikasi chat. Algoritma ini menggunakan operasi matematika dan nilai parameter dari kurva eliptik untuk menghasilkan kunci serta ciphertextnya dan juga melakukan dekripsi. Dari hasil ujicoba dan analisa implementasi enkripsi dan dekripsi menggunakan algoritma ECC, algoritma tersebut cocok digunakan sebagai metode enkripsi End-to-end, karena ukuran kunci yang relatif ringan dan operasi matematika yang menggunakan parameter khusus yang berbeda-beda. Hasil pengujian enkripsi dan dekripsi menggunakan parameter kurva eliptik secp192r1 dan secp192k1 yang mempunyai ukuran kunci sekitar 2¹⁹² bit, menghasilkan kunci dan ciphertext paling ringan dan paling cepat diproses, dengan angka nilai keduanya berukuran sepanjang 58 digit.

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ABSTRACTThe main purpose of communication security is to prevent message data from third party access. The solution to this problem is to implement End-to-end encryption. Elliptic Curve Cryptography (ECC) encryption algorithm is suitable for use as an End-to-end encryption method on digital communication systems including chat applications. ECC is a type of public key cryptography that bases its security on mathematical problems from elliptic curves, ECC has a level of security equals to RSA while using smaller keys. This study discusses the design and implementation of encryption and decryption algorithms that apply ECC cryptography as an End-to-end encryption method in chat applications. This algorithm uses mathematical operations and parameter values from the elliptic curve to generate keys and their ciphertext and also decrypt them. From the results of testing and analyzing the implementation of encryption and decryption using the ECC algorithm, the algorithm is suitable for use as an End-to-end encryption method, because of the relatively light key size and mathematical operations that use different parameters. The results of encryption and decryption testing using elliptic curve parameters secp192r1 and secp192k1 which have a key size of about 2¹⁹² bits, produce the lightest and fastest to process ciphertext and keys, with the value of both measuring 58 digits.

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Bitcoin adalah suatu sistem pembayaran elektronik. Proses transaksi dengan menggunakan bitcoin dilakukan tanpa otoritas sentral atau bank. Hal ini bertujuan untuk memotong biaya mediasi (mediation cost) dan juga membuat transaksi lebih praktis. Setiap pengguna bitcoin memiliki username sebagai kunci publik dan password sebagai kunci privatnya. Transaksi pada bitcoin memanfaatkan Elliptic Curve Digital Signature Algorithm (ECDSA). Adapun elliptic curve yang digunakan adalah secp256k1. Ada kriteria yang digunakan untuk menentukan tingkat keamanan kriptografi elliptic curve, salah satunya adalah kriteria safe curve yang diajukan oleh Bernstein dan Lange pada tahun 2013. Kriteria ini dibuat untuk menjamin keamanan kriptografi elliptic curve, tidak hanya menjamin keamanan Elliptic Curve Digital Logarithm Problem (ECDLP). Persyaratan suatu kurva merupakan safe curve meliputi persyaratan parameter dasar, persyaratan keamanan ECDLP (meliputi ketahanan dari serangan Rho dan transfer, diskriminan lapangan perkalian kompleks pada elliptic curve, dan rigidity), dan persyaratan keamanan kriptografi elliptic curve (meliputi penggunaan ladder Montgomery, ketahanan dari serangan twist, kelengkapan perkalian skalar, indistinguishability). Tujuan dari penelusuran literatur ini adalah untuk menjelaskan penggunaan secp256k1 pada transaksi bitcoin dan menganalisis kriteria safe curve yang tidak dipenuhi oleh secp256k1. Dari penelusuran literatur ini, dapat disimpulkan bahwa setiap pemilik bitcoin yang mentransfer bitcoin melakukan tanda tangan secara digital pada hash dari transaksi sebelumnya dan kunci publik pemilik berikutnya. Penandatanganan digital ini dilakukan dengan menggunakan kunci privat orang yang mentransfer bitcoin. Tanda tangan digital dapat diverifikasi menggunakan kunci publik pengguna yang mentransfer bitcoin. Pembentukan kunci publik dan kunci privat, pembentukan tanda tangan digital, dan verifikasi tanda tangan digital memanfaatkan elliptic curve digital signature algorithm (ECDSA), dengan elliptic curve yang digunakan adalah secp256k1. Secp256k1 tidak memenuhi persyaratan nilai minimum diskriminan lapangan perkalian kompleks pada E(F_p ) karena memiliki nilai |D|=2^1.6<2^100. Secp256k1 tidak memenuhi persyaratan penggunaan ladder Montgomery, kelengkapan perkalian skalar, dan indistinguishability karena secp256k1 memiliki cofactor h=1.

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Bitcoin is an electronic payment system. The transaction process by using Bitcoin is made without a central authority or bank. It has a purpose to cut mediation costs and also make transactions more practical. Every Bitcoin user has a username as a public key and password as its private key. Transactions on Bitcoin utilize the Elliptic Curve Digital Signature Algorithm (ECDSA). Specifically, the elliptic curve used is secp256k1. There are criteria used to determine the level of cryptographic security of an elliptic curve, one of which is the safe curve criteria proposed by Bernstein and Lange in 2013. These criteria are established not only to guarantee the security of Elliptic Curve Digital Logarithm Problems (ECDLP), but also to guarantee the safety of elliptic curve cryptography. The requirements for a curve are a safe curve including basic parameter requirements, ECDLP security requirements (including resistance to Rho and transfer attacks, complex multiplication field discriminant, and rigidity), and elliptic curve cryptography security requirements (including the use of Montgomery ladders, resistance to twist, completeness of scalar multiplication, and indistinguishability). The purposes of this literature review are to explain how to use secp256k1 in Bitcoin transactions and to analyse not-satisfying of the safe curve criteria on secp256k1. It can be concluded that each owner transfers bitcoin to the next owner by signing a hash from previous transaction and the public key of the next owner. The process of private key and public key generation, digital signature, and verification utilize Elliptic Curve Digital Signature Algorithm (ECDSA). The elliptic curve used is secp256k1. The reason Secp256k1 does not meet the requirements of minimum complex field discriminant value of E(F_p) is it has |D|=2^1.6<2^100. Secp256k1 does not use Montgomery ladder and also does not meet the requirement of completeness of scalar multiplication and indistinguishability because it has cofactor 1.

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"This research addresses the problem of finding a minimum Hamming Weight by proposing a left-to-right recoding of integers (from the most significant bit to the less significant one). This representation is the enhanced and modified version of a well-known recoding method called Generalized Non-Adjacent Form (G-NAF). Scanning the digits from the left-to-right is called Modified Generalized Signed Digit Non-Adjacent Form (MGSDNAF), which unlike the G-NAF, presents the ‘nice property’ to be obtained. A ‘nice property’ is one that is based on intuition and is particularly desirable to be obtained in a given context. This processing direction is of great importance because a table of pre-computed values may be used to speed up the scalar multiplication only for that direction. A subsequent advantage is that recoding the exponent in advance is not required. This results in better performances in both running time and memory space. This representation method can reduce the Hamming Weight of integers from about 21.6% for radix 3 to 15.1% for radix 9. These numbers for G-NAF recoding are 16.7% and 8.9% respectively. Comparing these numbers together shows that efficiency of the proposed method in reducing the Hamming Weight is more than the efficiency of G-NAF, which is from 30% (for radix 3) to more than 65% (for radix 9) more efficient in reducing the Hamming Weight. Finally, two radix 3 single scalar multiplication methods for Elliptic Curve Cryptography (ECC), which are based on G-NAF and Left-to-Right MGSDNAF, are compared in order to examine the application of the proposed method in cryptography. The results show that the proposed method can reduce the number of underlying arithmetic operations in single scalar multiplication by 14.1% while G-NAF can only reduce this number by 11.5%."