'Modular exponentiation' presentation slideshows

RSA Implementation Attacks

911 views • 73 slides

RSA Implementation Attacks

RSA Implementation Attacks. RSA. RSA Public key : (e,N) Private key : d Encrypt M C = M e (mod N) Decrypt C M = C d (mod N). Digital signature Hash M then sign In protocols, sign M itself: S = M d (mod N). Implementation Attacks. Attacks on RSA implementation

1.05k views • 73 slides

Addition

Addition. How fast can you add A+B. Addition. How fast can you add A+B. 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1. Addition. How fast can you add A+B. 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0. Addition. How fast can you add A+B. 1 0 1 0 1 1 1 0 0 1

630 views • 58 slides

Primes and Related Congruence Equations

Primes and Related Congruence Equations. 23 Sep 2013. Chapter 9. Objectives. ? To introduce prime numbers and their applications in cryptography. ? To discuss some primality test algorithms and their efficiencies.

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Modular Exponentiation

Modular Exponentiation. Modular Exponentiation. We do NOT compute C := M e mod n By first computing M e And then computing C := ( M e ) mod n Temporary results must be reduced modulo n at each step of the exponentiation. Modular Exponentiation. M 15

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Internet Key Exchange

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Pretty Good Privacy

544 views • 32 slides

CRT RSA Algorithm Protected Against Fault Attacks

Arnaud BOSCHER Spansion EMEA Robert NACIRI Oberthur Card Systems Emmanuel PROUFF Oberthur Card Systems. CRT RSA Algorithm Protected Against Fault Attacks. WISTP - 5/10/07. Agenda. RSA and Physical Attacks Modular Exponentiation Algorithm Resistant against Physical Attacks

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RSA Key Extraction via Low-Bandwidth Acoustic Cryptanalysis

RSA Key Extraction via Low-Bandwidth Acoustic Cryptanalysis. Daniel Genkin , Adi Shamir, Eran Tromer. Mathematical Attacks. Crypto Algorithm. Input. Output. Key. Goal: recover the key given access to the inputs and outputs . Side Channel Attacks. Radiation. Heat. EM. Sound.

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Lecture 2 Aug 28 goals: Introduction to recursion

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Number Theory

Number Theory. ??? School of Information Technology Sungshin W. University. Division.

494 views • 23 slides

MA/CSSE 473 Day 05

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Public key ciphers 2

Public key ciphers 2. Session 6. Contents. The discrete logarithm problem The Diffie-Hellman key exchange. The discrete logarithm problem. Over the real numbers, exponentiation (finding y = b x ) is not significantly easier than the inverse operation (finding x = log b ( y ))

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Implementing a 1024-bit RSA on FPGA

Implementing a 1024-bit RSA on FPGA. Jing Lu Qian Wan. Outline. Motivation System Architecture Implementation Testing. Motivation. Network hosts and devices are threatened by virus, worms, and all sorts of attacks

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DTTF/NB479: Dszquphsbqiz Day 9

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Chapter 3

Chapter 3. 3.6 Integers and Algorithms Representations of integers Algorithms for integer operations Modular Exponentiation The Euclidean Algorithm. Representations of integers.

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2014 ? ??? ????? ??????? ???

???? (Discrete Mathematics) ?? ???? (Recursive Algorithms). 2014 ? ??? ????? ??????? ???. Introduction. Recursive Algorithms. Recursive definitions can be used to describe algorithms as well as functions and sets. ( ??? ??? ??? ?? , ??? ????? ?? / ???? ??? ? ?? .)

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Hardware-Software Codesign of RSA for Optimal Performance vs. Flexibility Trade-off

Hardware-Software Codesign of RSA for Optimal Performance vs. Flexibility Trade-off. Malik Umar Sharif, Rabia Shahid , Marcin Rogawski , and Kris Gaj George Mason University USA. Supported in part by NIST/U.S . Department of Commerce under Grant No. 60NANB15D058.

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Announcements: HW3 updated. Due next Thursday Written quiz tomorrow on chapters 1-2 (next slide) Computer quiz next wee

278 views • 11 slides

Remaining course content Remote, fair coin flipping

DTTF/NB479: Dszquphsbqiz Day 33. Remaining course content Remote, fair coin flipping Presentations: Protocols, Elliptic curves, Info Theory, Quantum Crypto, Bitcoin , Error-correcting codes, Digital Cash Announcements: See schedule for weeks 9 and 10 Project workdays, exam

185 views • 8 slides