Understanding_Cryptography_Chptr_7---The_RSA_Cryptosystem

Understanding_Cryptography_Chptr_7---The_RSA_Cryptosystem -...

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Understanding Cryptography – A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 7 – The RSA Cryptosystem ver. December 7, 2010 These slides were prepared by Benedikt Driessen, Christof Paar and Jan Pelzl
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2 /34 Chapter 7 of Understanding Cryptography by Christof Paar and Jan Pelzl U Some legal stuff (sorry): Terms of use The slides can used free of charge. All copyrights for the slides remain with Christof Paar and Jan Pelzl. The title of the accompanying book “Understanding Cryptography” by Springer and the author’s names must remain on each slide. If the slides are modified, appropriate credits to the book authors and the book title must remain within the slides. It is not permitted to reproduce parts or all of the slides in printed form whatsoever without written consent by the authors.
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3 /34 Chapter 7 of Understanding Cryptography by Christof Paar and Jan Pelzl U Content of this Chapter The RSA Cryptosystem Implementation aspects Finding Large Primes Attacks and Countermeasures Lessons Learned
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4 /34 Chapter 7 of Understanding Cryptography by Christof Paar and Jan Pelzl U Content of this Chapter The RSA Cryptosystem Implementation aspects Finding Large Primes Attacks and Countermeasures Lessons Learned
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5 /34 Chapter 7 of Understanding Cryptography by Christof Paar and Jan Pelzl U The RSA Cryptosystem Martin Hellman and Whitfield Diffie published their landmark public- key paper in 1976 Ronald R ivest, Adi S hamir and Leonard A dleman proposed the asymmetric RSA cryptosystem in1977 Until now, RSA is the most widely use asymmetric cryptosystem although elliptic curve cryptography (ECC) becomes increasingly popular RSA is mainly used for two applications Transport of (i.e., symmetric) keys (cf. Chptr 13 of Understanding Cryptography ) Digital signatures (cf. Chptr 10 of Understanding Cryptography )
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6 /34 Chapter 7 of Understanding Cryptography by Christof Paar and Jan Pelzl U Encryption and Decryption RSA operations are done over the integer ring Z n (i.e., arithmetic modulo n), where n = p * q, with p, q being large primes Encryption and decryption are simply exponentiations in the ring In practice x, y, n and d are very long integer numbers ( 1024 bits) The security of the scheme relies on the fact that it is hard to derive the „private exponent“ d given the public-key ( n, e ) Definition Given the public key (n,e) = k pub and the private key d = k pr we write y = e k pub (x) x e mod n x = d k pr (y) y d mod n where x, y ε Z n. We call e k pub () the encryption and d k pr () the decryption operation.
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7 /34 Chapter 7 of Understanding Cryptography by Christof Paar and Jan Pelzl U Key Generation Like all asymmetric schemes, RSA has set-up phase during which the private and public keys are computed Remarks: Choosing two large, distinct primes p, q (in Step 1) is non-trivial
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Understanding_Cryptography_Chptr_7---The_RSA_Cryptosystem -...

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