RSA와 타원곡선암호의 성능 비교 분석
A Comparative Analysis of Performance Between RSA and Elliptic Curve Cryptography
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초록
본 논문에서는 RSA와 타원곡선암호의 비교 분석을 제시한다. 현재 디지털 암호 및 공개 키 암호화 부문에서 많은 연구들은 RSA 기반 암호화 시스템으로 수행되고, 타원 곡선을 기반으로 한 암호화 시스템은 RSA 암호화 시스템의 대안으로 제시된다. RSA 암호 시스템의 보안은 정수 인수분해 문제(IFP)를 기반으로 하는 반면, 타원곡선암호의 보안은 타원 곡선의 이산 로그 문제를 기반으로 한다. 타원곡선암호에 대한 중요한 관심은 타원 곡선의 이산 로그 문제를 해결하는 가장 잘 알려진 알고리즘이 꽉찬 지수 시간이 걸리는 반면 RSA의 정수 인수분해 문제를 해결하는 데는 일부 지수 시간이 걸린다는 것이다. 동일 수준의 보안에서 RSA보다 타원곡선암호에서 훨씬 더 작은 매개변수를 사용할 수 있음을 입증한다. RSA 알고리즘에는 2048비트의 키 크기가 필요한 반면 타원곡선암호에는 224비트의 키 크기가 필요하다. 보안 수준 비트가 80비트, 112비트, 128비트, 192비트, 256비트 데이터에 대한 암호화 및 복호화 시간을 기준으로 RSA와 타원곡선암호의 성능을 비교분석하여 제시한다. 이 분석에 따르면 타원곡선암호는 RSA보다 적은 메모리를 사용하며 특히 메모리가 제한된 장치에서는 RSA보다 우수하다.
Abstract
In this paper, we present a comparative analysis of elliptic curve cryptography and RSA known as one of the public key encryption algorithm methods. Currently, much research in the field of digital cryptography and public key cryptography is conducted with encryption systems based on public key cryptography algorithms, and encryption systems based on elliptic curves are presented as an alternative to public key encryption systems. The efficiency of an encryption algorithm is determined by several parameters, one of which is the length of the key. In order to provide strong security, public key cryptography systems use larger key sizes, and larger key sizes allow degradation of processing performance. As a result, processing speed decreases and memory usage increases. The encryption algorithms with small key sizes and high security are increasingly required in the end. The security of public key cryptography systems is based on the integer factorization problem, while the security of elliptic curve cryptography is based on the discrete logarithm problem of elliptic curves. An important concern about elliptic curve cryptography is that the best known algorithms for solving the discrete logarithm problem of elliptic curves take full exponential time, while solving integer factorization in public key cryptography takes partial exponential time. We demonstrate that much smaller parameters can be used in elliptic curve cryptography than in public key cryptography systems at the same level of security. We present a comparative analysis of performance and security based on key length comparison and encryption and decryption time for data according to security strength in public key cryptography systems and elliptic curve cryptography.
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