Statistical analysis of pollard's rho attack on elliptic curve cryptography = analisa statistik dari serangan pollard's rho untuk kriptografi kurva eliptik

Josodipuro, Madeleine Jose (2020) Statistical analysis of pollard's rho attack on elliptic curve cryptography = analisa statistik dari serangan pollard's rho untuk kriptografi kurva eliptik. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Elliptic curve cryptography is a relatively new public-key cryptography mechanism which has been becoming more popular in recent years. With its ability to provide the same level of security as its predecessor, the RSA, with a shorter key length, it is no wonder that its usage has been increasing in various fields using different cryptographic protocols, such as Elliptic Curve Diffie-Hellman (ECDH), Elliptic Curve Digital Signature Algorithm (ECDSA) and the ElGamal encryption scheme. Several attacks have been developed to solve the elliptic curve discrete logarithm problem. These attacks can be categorised into side-channel, special-purpose and general-purpose attacks. One of the most practical generic attacks is the Pollard's Rho algorithm, which originates as an algorithm for prime factorisation. Many studies have proposed on how to improve this algorithm through different methods. This thesis will also attempt to provide a statistical insight on how various factors, namely the private-public key pairs and parameters within the sequence used in Pollard's Rho algorithm, may affect the performance speed of the algorithm. This will be done using the ANOVA statistical test. / Kriptografi kurva eliptik adalah mekanisme kriptografi kunci publik yang relatif baru dan telah menjadi lebih populer dalam beberapa tahun terakhir. Dengan kemampuannya untuk memberikan tingkat keamanan yang sama dengan pendahulunya, RSA, dengan panjang kunci yang lebih pendek, tidak mengherankan bahwa penggunaannya telah meningkat di berbagai bidang menggunakan protokol kriptografi berbeda, seperti Elliptic Curve Diffie-Hellman (ECDH), Elliptic Curve Digital Signature Algorithm (ECDSA) dan skema enkripsi ElGamal. Beberapa serangan telah dikembangkan untuk memecahkan masalah logaritma diskrit kurva eliptik. Serangan-serangan ini dapat dikategorikan ke dalam serangan side-channel, tujuan khusus dan tujuan umum. Salah satu serangan generik yang praktis adalah algoritma Pollard's Rho, yang berasal sebagai algoritma untuk faktorisasi prima. Banyak penelitian telah mengusulkan cara memperbaguskan algoritma ini melalui metode yang berbeda. Skripsi ini juga akan berusaha untuk memberikan wawasan statistik tentang bagaimana berbagai faktor, yaitu pasangan kunci privat-publik dan parameter dalam barisan yang digunakan dalam algoritma Pollard's Rho, dapat mempengaruhi kecepatan kinerja algoritma ini. Ini akan dilakukan dengan menggunakan uji statistik ANOVA.

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