• unknown (b.)


A Professor of Computer Science, he is a computer scientist and mathematician. He has proved (while at IBM Zurich) a lower bound to the computational complexity of generic algorithms for solving the discrete logarithm problem, a problem in group theory which is of considerable importance to public-key cryptography. He received his B.S. degree in 1983, from the University of Wisconsin-Eau Claire and his M.S. degree in 1985, from the University of Wisconsin–Madison. He obtained his PhD in Computer Science also from the University of Wisconsin–Madison in 1989. He is a Professor at the Courant Institute of Mathematical Sciences at New York University (NYU) in New York City, NY, focusing on algorithm and cryptography courses. He has held positions at AT&T Bell Labs, the University of Toronto, Saarland University, and the IBM Zurich Research Laboratory. His main research interests and contributions are computer algorithms relating to number theory, algebra, and cryptography. The Cramer–Shoup cryptosystem asymmetric encryption algorithm developed in 1998, and which bears his name is an asymmetric key encryption algorithm, and was the first efficient scheme proven to be secure against adaptive chosen ciphertext attack using standard cryptographic assumptions. Its security is based on the computational intractability (widely assumed, but not proved) of the decisional Diffie–Hellman assumption. Developed along with Ronald Cramer, it is an extension of the Elgamal cryptosystem. In contrast to Elgamal, which is extremely malleable, Cramer–Shoup adds other elements to ensure non-malleability even against a resourceful attacker. This non-malleability is achieved through the use of a universal one-way hash function and additional computations, resulting in a ciphertext which is twice as large as in Elgamal. His freely available (under the terms of the GNU GPL) C++ library of number theory algorithms, NTL, is widely used and well regarded for its high performance. He is the author of a widely used textbook, “A Computational Introduction to Number Theory and Algebra”, Cambridge university press It is freely available online. A few of the latest publications of which he is the author or co-author include: “Sequences of games: a tool for taming complexity in security proofs”, IACR Cryptology ePrint Archive 2004, 332; “Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack” with R Cramer, SIAM Journal on Computing 33 (1), 167-226; “Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption” with R Cramer, Advances in Cryptology—Eurocrypt 2002, 45-64; “Optimistic fair exchange of digital signatures” with N Asokan, and M Waidner, Selected Areas in Communications, IEEE Journal on 18 (4), 593-610; and “Practical verifiable encryption and decryption of discrete logarithms” with J. Camenisch, Advances in Cryptology-CRYPTO 2003, 126-144. He is also closely involved in the development of an emerging ISO standard for public-key cryptography.
  • Noted For:

    Co-developer of The Cramer–Shoup cryptosystem asymmetric encryption algorithm, the first efficient scheme proven to be secure against adaptive chosen ciphertext attack using standard cryptographic assumptions
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