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Shafi Goldwasser

Shafi Goldwasser (born 1959) is an American-Israeli computer scientist renowned for her foundational contributions to modern cryptography, computational complexity theory, and related fields such as probabilistic algorithms and computational number theory.^[1] She holds the position of RSA Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology (MIT), where she has been a faculty member since 1983, the C. Lester Hogan Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley, and is also a professor of computer science and applied mathematics at the Weizmann Institute of Science in Israel, a role she has held since 1993.^[2] Goldwasser's work has revolutionized the theoretical underpinnings of secure communication and computation, establishing key concepts like provable security that underpin contemporary cryptographic systems.^[3] Goldwasser earned her B.S. in mathematics from Carnegie Mellon University in 1979, followed by an M.S. and Ph.D. in electrical engineering and computer science from the University of California, Berkeley in 1981 and 1984, respectively, under the supervision of Manuel Blum.^[1] Early in her career, she completed a postdoctoral fellowship at MIT in 1983 and advanced rapidly to full professorship there in 1992, later becoming the RSA Professor in 1997 to honor her impact on public-key cryptography.^[1] From 2018 to 2024, she served as director of the Simons Institute for the Theory of Computing at UC Berkeley, fostering interdisciplinary research in theoretical computer science during her tenure.^[2] Her most influential contributions include co-developing zero-knowledge proofs with Silvio Micali and Charles Rackoff in the 1980s, which enable verification of statements without revealing underlying secrets—a cornerstone of secure protocols used in digital signatures, authentication, and blockchain technologies.^[3] Goldwasser also pioneered probabilistic encryption schemes, interactive proof systems, and advancements in primality testing, such as the elliptic curve primality proving algorithm, alongside work on property testing and hardness of approximation in complexity theory.^[1] These innovations earned her the 2012 ACM A.M. Turing Award, often called the "Nobel Prize of computing," shared with Micali for transforming cryptography from an ad hoc practice into a rigorous mathematical discipline.^[1] Among her numerous honors are two Gödel Prizes (1993 and 2001), the Grace Murray Hopper Award (1996), the Benjamin Franklin Medal (2010), the L’Oréal-UNESCO For Women in Science Award (2021), election as a Fellow of the Royal Society in 2023, and election to the American Academy of Arts and Sciences in 2025.^[3]^[4]

Early Life and Education

Early Life

Shafi Goldwasser was born on November 14, 1959, in New York City to Israeli immigrant parents, holding dual Israeli-American citizenship through her family heritage.^[1] Her father hailed from Poland, while her mother was born in Kfar Vitkin, Israel, and the family included an older brother and a younger sister.^[5] Goldwasser spent her early childhood in Sea Gate, a beach community near New York City, before moving to Tel Aviv, Israel, at the age of six, where she attended the A.D. Gordon School starting in first grade.^[5] Raised in a Jewish-Israeli household that blended American and Israeli cultural influences, she experienced a formative environment emphasizing pragmatism and intellectual curiosity.^[5]^[6] Her early interest in mathematics and science was shaped by her family's strong emphasis on education and encouragement to pursue scientific fields, though she initially enjoyed literature and history in elementary school before shifting focus to math and physics during high school.^[7]^[5] While specific pre-college exposure to computing concepts is not documented, her foundational passion for exact sciences laid the groundwork for later academic pursuits, leading her to enroll at Carnegie Mellon University.^[7]

Formal Education

Shafi Goldwasser earned a Bachelor of Science degree in mathematics from Carnegie Mellon University in 1979.^[1] She then pursued graduate studies in computer science at the University of California, Berkeley, where she received a Master of Science degree in 1981.^[1] Goldwasser completed her PhD in computer science at Berkeley in 1984.^[1] Her doctoral research was supervised by Manuel Blum.^[8] During her time as a graduate student, Goldwasser collaborated closely with fellow PhD student Silvio Micali, also advised by Blum, on foundational concepts in cryptography.^[8] This early partnership produced influential work, including the introduction of probabilistic encryption schemes that addressed semantic security in public-key systems.^[9]

Professional Career

Academic Positions

Goldwasser joined the Massachusetts Institute of Technology (MIT) faculty in 1983 as an Assistant Professor in the Department of Electrical Engineering and Computer Science, following her postdoctoral fellowship at the institution.^[1]^[10] She was promoted to Associate Professor in 1987 and advanced to full Professor in 1992.^[10] In 1997, she became the first holder of the RSA Professorship in Electrical Engineering and Computer Science at MIT, a distinguished chair she has retained since.^[11]^[12] In 1993, Goldwasser was appointed Professor of Computer Science and Applied Mathematics at the Weizmann Institute of Science in Rehovot, Israel, where she has continued to serve.^[10]^[13] In 2018, she joined the University of California, Berkeley as Professor of Electrical Engineering and Computer Sciences (EECS).^[14] As of 2025, Goldwasser maintains her professorial roles at MIT, the Weizmann Institute, and UC Berkeley, actively supervising PhD students in cryptography at these institutions.^[12]^[13]^[15]^[16]

Industry and Leadership Roles

Goldwasser has held prominent leadership positions in computational research institutions beyond her academic appointments at MIT, the Weizmann Institute, and UC Berkeley. From January 2018 to August 2024, she served as director of the Simons Institute for the Theory of Computing at the University of California, Berkeley, where she oversaw programs advancing theoretical computer science, including workshops on cryptography and quantum computing.^[2]^[17] Since 2024, she has served as Co-Director of the Resilience Pod at the Simons Institute.^[18] In the private sector, Goldwasser co-founded Duality Technologies in 2016 and has acted as its chief scientist, developing technologies for privacy-preserving data analytics using advanced cryptographic methods like homomorphic encryption to enable secure data collaboration without exposing sensitive information.^[19]^[20] The company focuses on applications in industries such as finance and healthcare, addressing data privacy challenges in collaborative analytics. Goldwasser's interdisciplinary engagements extend to innovative scientific initiatives. Starting in 2021, she joined Project CETI (Cetacean Translation Initiative) as lead for theoretical analysis, applying machine learning and computational techniques to decode sperm whale communication patterns, such as codas, to advance understanding of nonhuman intelligence.^[21] In January 2024, she participated in the UC Noyce Initiative, securing funding for projects on quantum computation, including efforts to design modular quantum processors for enhanced processing speeds.^[22] Additionally, on June 22, 2023, she was appointed to the advisory board of ADIA Lab in Abu Dhabi, contributing expertise in cryptography and AI to guide research in foundational technologies.^[23]

Research Contributions

Foundations of Cryptography

Shafi Goldwasser played a pivotal role in establishing cryptography as a rigorous mathematical discipline during the 1980s, shifting the field from ad-hoc engineering approaches to complexity-theoretic foundations that emphasize provable security under computational assumptions. This transformation, largely through her collaborations, integrated concepts from computational complexity theory to analyze cryptographic primitives, ensuring their resistance to attacks by computationally bounded adversaries. In 1984, Goldwasser collaborated with Silvio Micali to introduce probabilistic encryption, a paradigm that encrypts the same plaintext differently each time to thwart chosen-plaintext attacks. Their work defined semantic security, a stringent notion where an adversary, even after choosing ciphertexts, gains negligible information about the underlying plaintext beyond its length. This security model protects against adaptive adversaries by requiring that ciphertexts are computationally indistinguishable for different messages, formalized using the quadratic residuosity assumption. Central to their contribution is the Goldwasser-Micali cryptosystem, the first provably secure probabilistic public-key scheme based on the hardness of distinguishing quadratic residues modulo a composite number. In this system, key generation involves selecting two large primes p and q to form a Blum integer N = pq, where the public key is N and the private key is (p, q). To encrypt a bit b \in \{0, 1\}, a random x \in \mathbb{Z}_N^\times is chosen such that \gcd(x, N) = 1, and the ciphertext is the pair (x, y) where y = x^2 \cdot (-1)^b \mod N. Decryption determines b by checking the Legendre symbol of y / x^2 \mod N using the factorization of N; if it is a quadratic residue (Legendre symbol 1), then b = 0, otherwise b = 1. Security relies on the quadratic residuosity problem, assumed intractable without knowledge of the factors of N. Building on these ideas, Goldwasser's 1985 paper with Micali and Charles Rackoff, "The Knowledge Complexity of Interactive Proof Systems," introduced the concept of knowledge complexity, quantifying the information leaked during interactive protocols.^[24] This metric measures how much "knowledge" a verifier gains from a prover beyond the validity of the statement, laying groundwork for zero-knowledge properties where no additional information is revealed.^[24] The paper formalized interactive proofs as probabilistic polynomial-time protocols between a computationally unbounded prover and a bounded verifier, defining soundness, completeness, and zero-knowledge in complexity-theoretic terms.^[24] These definitions enabled rigorous analysis of cryptographic protocols, influencing subsequent developments in secure computation.

Interactive Proofs and Zero-Knowledge

Shafi Goldwasser, along with Silvio Micali and Charles Rackoff, introduced the concept of interactive proof systems in 1985, formalizing a framework where a computationally bounded verifier can be convinced of the truth of a statement by an all-powerful prover through a series of interactive messages, without the verifier learning anything beyond the statement's validity.^[25] This work built on earlier ideas like probabilistic encryption, which provided a foundation for privacy-preserving computations. They defined key properties for these systems: completeness, ensuring that if the statement is true, the honest prover convinces the verifier with high probability; soundness, guaranteeing that if the statement is false, no prover can convince the verifier except with negligible probability; and zero-knowledge, meaning the verifier gains no additional knowledge beyond the statement's correctness, formalized through simulation where any verifier's view can be indistinguishably simulated without prover interaction.^[25] In their seminal paper, Goldwasser, Micali, and Rackoff demonstrated the existence of zero-knowledge proofs for languages in NP, such as graph non-isomorphism, where the prover convinces the verifier that two graphs are non-isomorphic without revealing a distinguishing isomorphism or witness.^[25] They proved that these properties hold under computational assumptions, establishing zero-knowledge as a transformative tool for privacy in verification. Building on this, Goldwasser and Micali, in collaboration with Avi Wigderson in 1986, extended zero-knowledge proofs to all languages in NP using auxiliary assumptions like the existence of one-way functions, showing that zero-knowledge proofs are broadly applicable and can be made honest-verifier zero-knowledge, further strengthening the simulation paradigm.^[26] Goldwasser and Micali further contributed to the study of public-coin interactive protocols in 1986, defining Arthur-Merlin protocols where the verifier (Arthur) sends random coin flips publicly to the prover (Merlin), who then responds; this led to the definition of the AM complexity class, encompassing sets verifiable by constant-round probabilistic public-coin protocols with bounded error. These protocols simplified the interactive proof model by restricting verifier messages to randomness, proving that AM captures a broad class of verifiable languages while preserving soundness and completeness. Later work by Goldwasser and Michael Sipser showed that interactive proofs with private coins are equivalent in power to public-coin ones like Arthur-Merlin protocols, unifying the models.^[27] The practical applications of these zero-knowledge proofs emerged prominently in authentication and identification schemes. Goldwasser, Micali, and Rackoff's framework enabled protocols where a prover authenticates without revealing secrets, directly influencing identification systems. A key development was the Fiat-Shamir heuristic, introduced in 1986, which transforms interactive zero-knowledge proofs into non-interactive ones by replacing verifier challenges with hash function outputs, allowing efficient signature and identification schemes based on discrete log assumptions. This heuristic, combined with zero-knowledge constructions, facilitated secure authentication in resource-constrained settings, such as smart cards, without exposing private keys. In a major advancement, Goldwasser's foundational work on interactive proofs culminated in the 1988 theorem establishing that IP, the class of problems with polynomial-round interactive proofs, equals PSPACE, the class of problems solvable in polynomial space. This result, achieved through collaborations including Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan, demonstrated that interactive proofs can verify any PSPACE-complete problem, such as quantified Boolean formulas, using algebraic techniques like sum-check protocols over multivariate polynomials. The theorem highlighted the expressive power of interactive proofs, showing they capture a vast portion of computational complexity beyond NP, with Goldwasser's earlier definitions providing the essential framework for these probabilistic verifications.

Primality Testing and Number Theory

In collaboration with Joe Kilian, Shafi Goldwasser developed a foundational algorithm for primality testing using elliptic curves, detailed in their 1999 Journal of the ACM paper.^[28] This method, known as elliptic curve primality proving (ECPP), provides a probabilistic test that generates short, verifiable certificates of primality specifically for prime inputs, enabling efficient certification of large numbers.^[28] Unlike earlier probabilistic tests like Miller-Rabin, which offer no certificates, ECPP produces recursive proofs that can be deterministically verified, making it suitable for applications requiring provable primality. The algorithm operates by constructing a random elliptic curve E over the finite field \mathbb{F}_n, where n is the integer under test, and identifying a point P on E whose order q is a large prime approximately n/2 in size.^[28] If such a q is found and certified prime (via recursion on smaller instances), then n must be prime, as the group order \#E(\mathbb{F}_n) divides n-1 only if n is prime, leveraging properties from the theory of elliptic curves and complex multiplication.^[28] The recursion terminates when the subproblem size drops below a threshold verifiable by deterministic methods like trial division. The process relies on Schoof's algorithm for counting points on elliptic curves, ensuring polynomial-time steps per level.^[28] This yields a certificate of length O((\log n)^2), verifiable in time O((\log n)^4). The expected running time is polynomial, achieving O((\log n)^6) under heuristic assumptions on prime distributions, though unconditional bounds are O((\log n)^{11}).^[28] Subsequent refinements by Atkin and Morain rendered practical implementations deterministic by selecting curves with complex multiplication to avoid randomness. Goldwasser's broader contributions to computational number theory encompass constructing pseudorandom generators from hardness assumptions in number-theoretic problems, such as the difficulty of factoring or computing discrete logarithms. In joint work with Micali and Rackoff, she demonstrated how one-way functions based on quadratic residuosity modulo Blum integers can yield secure pseudorandom bit generators, expanding the toolkit for derandomization in number-theoretic settings. These generators stretch short seeds into long pseudorandom sequences indistinguishable from uniform randomness by polynomial-time adversaries, assuming the underlying hardness. These advancements have direct applications in cryptography, particularly for secure key generation in systems like RSA and Diffie-Hellman, where certified large primes are essential to prevent attacks exploiting composite moduli. ECPP's efficiency has enabled the verification of record-breaking primes, underpinning the security of modern public-key infrastructures.^[29]

Property Testing and Hardness of Approximation

Goldwasser made significant contributions to property testing, a subfield of algorithms that determines whether an object has a certain property or is far from having it, with minimal access to the object. In collaboration with Oded Goldreich and Dana Ron, she introduced the framework for testing combinatorial properties of functions and graphs in the late 1990s. Their 1998 paper, "Property Testing and its Connection to Learning and Approximation," formalized property testing for graph properties like connectivity and cycle-freeness, showing that many properties can be tested with query complexity independent of the input size, polylogarithmic in the size.^[30] This work established property testing as a distinct area, with applications in learning theory, streaming algorithms, and data analysis, influencing sublinear algorithms. In the area of hardness of approximation, Goldwasser's work advanced the understanding of the limits of approximation algorithms for NP-hard problems. She co-authored the 1991 paper "Interactive Proofs and the Hardness of Approximating Cliques" with Uriel Feige, László Lovász, Muli Safra, and Mario Szegedy, which used multi-prover interactive proofs to prove that approximating the maximum clique problem within a factor of n^{1-ε} is NP-hard for any ε > 0, under randomized reductions.^[31] This result was a cornerstone in the development of the PCP theorem and probabilistically checkable proofs, demonstrating that certain optimization problems remain hard even for approximate solutions. Her contributions in this domain, building on interactive proof systems, helped classify the approximability of problems like set cover and vertex cover, showing inapproximability gaps that hold unless P=NP.

Awards and Honors

Major Prizes

Shafi Goldwasser received the ACM A.M. Turing Award in 2012, shared with Silvio Micali, for their transformative contributions to the theory of computation, particularly in developing mathematically rigorous methods to design and analyze secure cryptographic systems, including interactive proofs, zero-knowledge proofs, and pseudorandom functions.^[1] This award, often called the "Nobel Prize of computing," recognizes their foundational work that established modern cryptography on secure theoretical grounds, enabling practical applications in secure communication and data protection.^[32] Goldwasser has been awarded the Gödel Prize twice by the Association for Computing Machinery (ACM) Special Interest Group on Algorithms and Computation Theory (SIGACT) and the European Association for Theoretical Computer Science (EATCS). In 1993, she shared the prize with László Babai, Shlomo Moran, Silvio Micali, and Charles Rackoff for their seminal papers on interactive proof systems, which introduced a new paradigm for verifiable computation where a prover can convince a verifier of a statement's truth without revealing underlying secrets, revolutionizing complexity theory and cryptography.^[33] In 2001, she shared the prize with Sanjeev Arora, Uriel Feige, Carsten Lund, László Lovász, Rajeev Motwani, Shmuel Safra, Madhu Sudan, and Mario Szegedy for their groundbreaking papers establishing the Probabilistically Checkable Proofs (PCP) theorem and its implications for the hardness of approximating NP-complete problems, such as the clique problem, which provided deep insights into the limits of efficient approximation algorithms.^[34] These awards highlight her enduring impact on theoretical computer science by bridging probabilistic methods with computational hardness. In 1996, Goldwasser received the ACM Grace Murray Hopper Award for her outstanding contributions to computer science as a young professional, particularly for pioneering work in cryptography and the development of probabilistic encryption and zero-knowledge proofs.^[35] In 2010, Goldwasser was awarded the Benjamin Franklin Medal in Computer and Cognitive Science by the Franklin Institute for her pioneering contributions to modern cryptography, including the invention of probabilistic encryption schemes that ensure semantic security against chosen-plaintext attacks, thereby laying the groundwork for secure digital systems.^[36] This medal underscores her role in transforming cryptography from an ad hoc practice into a rigorous science, influencing fields from secure internet protocols to blockchain technology. Goldwasser received the 2021 L'Oréal-UNESCO For Women in Science International Award for her pioneering and fundamental work in computer science, particularly in the mathematics of cryptography and the theory of computation, recognizing her as a leading figure in advancing secure and efficient algorithms.^[37] The award emphasizes her efforts to promote women in STEM and her innovations that protect data privacy in an increasingly digital world. In 2021, Goldwasser shared the FOCS Test of Time Award from the IEEE Symposium on Foundations of Computer Science for the 1991 paper "Approximating Clique is Almost NP-Complete," co-authored with Uriel Feige, László Lovász, Shmuel Safra, and Mario Szegedy, which demonstrated that approximating the maximum clique size in a graph within a factor of n^{1-ε} is NP-hard for any ε > 0, providing crucial evidence for the intractability of approximation problems central to complexity theory.^[38] This accolade celebrates the paper's lasting influence on understanding the boundaries of efficient algorithms for NP-hard optimization.

Fellowships and Honorary Degrees

Shafi Goldwasser was elected a Fellow of the Association for Computing Machinery (ACM) in 2017 for her foundational contributions to cryptography and theoretical computer science. She was elected to the National Academy of Engineering in 2005, recognizing her pioneering work in cryptography, complexity theory, and their applications to security. Goldwasser joined the National Academy of Sciences in 2004, honored for her advancements in computational number theory and probabilistic algorithms. In 2001, she was elected to the American Academy of Arts and Sciences, acknowledging her leadership in theoretical computer science and its interdisciplinary impacts.^[39] In 2025, Goldwasser was elected to the American Academy of Sciences and Letters for her outstanding contributions to scholarship in theoretical computer science.^[4] Internationally, Goldwasser was elected a Foreign Member of the Royal Society in 2023, celebrated for her transformative role in establishing modern cryptography as a rigorous mathematical discipline.^[3] Goldwasser has received numerous honorary degrees for her lifetime achievements. She was awarded an honorary Doctor of Science by the University of Oxford in 2019.^[40] In 2018, Carnegie Mellon University conferred an honorary degree upon her during its commencement, where she also delivered the keynote address.^[41] Additional honorary degrees include those from Ben-Gurion University, Bar-Ilan University, the University of Haifa, Tel Aviv University, and the University of Waterloo.^[3] In recognition of her mathematical contributions to cryptography, Goldwasser received the RSA Conference Award for Excellence in Mathematics in 1998.^[42]

Personal Life

Family and Background

Shafi Goldwasser was born Shafrira Goldwasser in 1959 in New York City to Israeli parents of Jewish heritage, granting her dual American-Israeli citizenship from birth.^[6] Her father, originally from Poland, survived World War II by escaping to Siberia before settling in Israel, while her mother was born and raised in the agricultural community of Kfar Vitkin, which her maternal family helped found in the 1930s.^[5] The family returned to Tel Aviv when Goldwasser was six years old, where she spent her formative years immersed in Israeli culture.^[5] Goldwasser's Jewish heritage played a role in shaping her intellectual pursuits, particularly through her childhood fascination with biblical stories, which fostered a narrative lens that later influenced her research style in theoretical computer science.^[5] She married computer scientist Nir Shavit in 1987 during a sabbatical in Israel, and the couple has two sons, Yonadav and Lior.^[5] Goldwasser maintains strong personal ties to Israel through her citizenship and long-standing position at the Weizmann Institute of Science in Rehovot, where she divides her time with her family, spending approximately three years at a stretch between there and the United States.^[5]

Recent Activities and Influence

Since 2016, Shafi Goldwasser has played a pivotal leadership role as co-founder and chief scientist at Duality Technologies, a company specializing in privacy-enhancing technologies that enable secure data collaboration without exposing sensitive information.^[19] Under her guidance, Duality has advanced secure multi-party computation (SMPC) protocols, allowing organizations to perform joint computations on encrypted data for applications in finance, healthcare, and AI, with notable developments including patented methods for privacy-preserving analytics as of 2023.^[43] This work builds on cryptographic foundations to address real-world privacy challenges in data sharing. Goldwasser has extended her influence to interdisciplinary areas, particularly the integration of cryptography with artificial intelligence to foster trust in machine learning systems. In her 2023-2024 lectures, such as the Harold Pender Award Lecture at the University of Pennsylvania titled "Constructing and Deconstructing Trust," she explored cryptographic tools to mitigate vulnerabilities like backdoor attacks and ensure privacy and robustness across ML pipelines, from data collection to model deployment.^[44] These presentations, including her 2025 Emmy Noether Lectures at the Institute for Advanced Study on "Trust and Distrust in ML: Privacy, Verification and Robustness," highlight ongoing efforts to apply zero-knowledge proofs and related techniques to verifiable AI.^[45] Throughout her career, Goldwasser has mentored numerous PhD students—according to academic genealogy records, she has directly supervised at least 11 doctoral candidates, many of whom have advanced to prominent roles in academia, industry, and research institutions, perpetuating her impact on theoretical computer science.^[46] Her broader legacy includes championing women in STEM, exemplified by her 2021 L'Oréal-UNESCO For Women in Science Award, which recognizes her contributions to science while promoting gender equity in technical fields.^[47]

References

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Shafi Goldwasser - A.M. Turing Award Laureate
Shafi Goldwasser has made fundamental contributions to cryptography, computational complexity, computational number theory and probabilistic algorithms.
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EMPLOYMENT AND VISITING POSITIONS. Massachusetts Institute of Technology. 1997-present. RSA Professor of Electrical Engineering and Computer Science.
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Shafrira Goldwasser. Department of Computer Science and Applied Mathematics. Email shafi.goldwasser@weizmann.ac.il. location Jacob Ziskind Building , Room 223.
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CETI is a nonprofit organization applying advanced machine learning and state-of-the-art robotics to listen to and translate the communication of sperm whales.
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László Babai, Shlomo Moran, and Shafi Goldwasser, Silvio Micali, Charles Rackoff. The 1993 Gödel Prize was shared by two papers,. László Babai and Shlomo Moran:
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Gödel Prize - 2001
Gödel Prize - 2001. Sanjeev Arora, Uriel Feige, Shafi Goldwasser, Carsten Lund, Laszlo Lovász, Ranjeev Motwani, Shmuel Safra, Madhu Sudan, Mario Szegedy.
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Shafrira Goldwasser. MathSciNet. Ph.D. University of California, Berkeley 1984 UnitedStates. Dissertation: Probabilistic Encryption: Theory and Applications.<|control11|><|separator|>
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Feb 12, 2021 · MIT Professor Shafi Goldwasser has been named the laureate for North America in this year's 2021 L'Oréal-UNESCO For Women in Science ...Missing: promoting | Show results with:promoting
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Computer Scientists Combine Two 'Beautiful' Proof Methods
Oct 4, 2024 · From top: Shafi Goldwasser, Silvio Micali and Charles Rackoff invented zero-knowledge proofs, which demonstrate that a statement is true without ...