Chapter 5 Security Technology5.2 Elliptic Curve Cryptography and RSA cryptography

In terms of encryption algorithms, RSA cryptography uses unique factorization from arithmetic theory forkey creation and data encryption and decryption; as a result, the encryption strength characteristics are such that the unique factorization questions are extremely difficult to solve. Calculations in the case of Elliptic Curve Cryp-tography is based on the points of an elliptic curve, resulting in encryption strength characteristics in which it isdifficult to solve the discrete logarithm problems from these points. In both of these schemes, it is extremely dif-ficult for a third party (cracker or hacker) to decipher the private key or plain text from the public key or cipher-text. Given these characteristics, a high level of security can be achieved through the use of either of theseschemes. There are many application examples of public key encryption schemes; RSA cryptography is currently inwide use on the Internet. RSA cryptography is used as the public key encryption method in smart cards as well, but problems arising from the processing time have led to increased interest in Elliptic CurveCryptography for these applications. In comparison to RSA cryptography, Elliptic Curve Cryptography has the following advantages: ?Equivalent encryption strength achieved with shorter key lengths Key lengths can be reduced significantlyby using Elliptic Curve encryption. For example, with a key length of 1024 bits in the case of RSA encryption,the equivalent key length using Elliptic Curve encryption would be 160 bits; with an RSA key length of2048 bits, the Elliptic Curve encryption key length would be 211 bits.?Reduced key length growth rate In the previous example, where the key length in the case of RSA encryption is doubled (1024 → 2048),the key length for Elliptic Curve encryption increases by only 1.3 × (160 → 211). ?Because of the shorter key length, processing time decreases, and higher encryption processing speedsbecome possible. ?Because the computation processing volumes are reduced, the scale of the hardware can be reduced as well. ?Elliptic Curve encryption is perfectly suited to improved encryption strength on the limited surfaces ofsemiconductor chips. Fujitsu has led the world with the commercial release of a microcontroller with on-board FRAM - an originalFRAM product with an embedded Elliptic Curve encryption coprocessor that incorporates next-generation Ellip-tic Curve encryption and FRAM into a single chip. For further details, refer to “Chapter 3 Introduction to FujitsuFRAM”. 29